Initial Conditions

x(t)

y(t)

Animate time

LL crnr

UR crnr

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y

x

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f(x, y) = (-4 * x) - (2 * y)
g(x, y) = (-1 * x) - (3 * y)
A = (1.2337904625833855, 3.804233948734322)
maxT = 9 (slider from 0 to 100, step 0.1)
stepsolve = 0.01 (slider from 0.00010 to 0.5, step 0.000010)
ppsol = SolveODE(g, f, x(A), y(A), maxT, stepsolve)
stepplot: 0.01
xlist = Sequence(x(Point[ppsol, tt]), tt, 0, 1, stepplot)
ylist = Sequence(y(Point[ppsol, tt]), tt, 0, 1, stepplot)
tlist: (Sequence[0, 1, stepplot] * maxT)
h = Ray((0, 0), (1, 0))
i = Ray((0, 0), (0, 1))
t = 2.94 (slider from -3 to maxT, step stepplot)
B = Point(ppsol, t / maxT)
X_t: (t, x(B))
Y_t: (t, y(B))
a = false
C = (-8.232832130488697, -5.447734317537779)
D = (8.06561415659846, 8.156311126618895)
H: abs(x(D) - x(C))
W: abs(y(D) - y(C))
n = 10 (slider from 1 to 30, step 1)
b = false
c = true
text1: "\frac{dx}{dt}=" + (LaTeX[f]) + " \\
\frac{dy}{dt}=" + (LaTeX[g]) + ""
InputBox1 = Textfield(f)
InputBox2 = Textfield(g)
mxval = Max(xlist)
myval = Max(ylist)
d = false
x2sol(x) = DataFunction[{0, 0.09, 0.18, 0.27, 0.36, 0.45, 0.54, 0.6300000000000001, 0.72, 0.8099999999999999, 0.8999999999999999, 0.9899999999999999, 1.0799999999999998, 1.1699999999999997, 1.2599999999999998, 1.3499999999999999, 1.44, 1.53, 1.62, 1.7100000000000002, 1.8000000000000003, 1.8900000000000003, 1.9800000000000004, 2.0700000000000007, 2.1600000000000006, 2.2500000000000004, 2.3400000000000007, 2.4300000000000006, 2.520000000000001, 2.6100000000000008, 2.700000000000001, 2.790000000000001, 2.8800000000000012, 2.970000000000001, 3.0600000000000014, 3.1500000000000012, 3.2400000000000015, 3.3300000000000014, 3.4200000000000017, 3.5100000000000016, 3.600000000000002, 3.6900000000000017, 3.780000000000002, 3.870000000000002, 3.960000000000002, 4.0500000000000025, 4.140000000000002, 4.230000000000002, 4.320000000000002, 4.410000000000003, 4.500000000000002, 4.590000000000002, 4.680000000000002, 4.770000000000002, 4.860000000000002, 4.950000000000003, 5.040000000000003, 5.130000000000003, 5.220000000000002, 5.310000000000002, 5.400000000000003, 5.490000000000003, 5.580000000000003, 5.6700000000000035, 5.760000000000003, 5.850000000000003, 5.940000000000003, 6.030000000000003, 6.120000000000004, 6.2100000000000035, 6.300000000000003, 6.390000000000004, 6.480000000000004, 6.570000000000004, 6.660000000000004, 6.7500000000000036, 6.840000000000004, 6.930000000000004, 7.020000000000004, 7.110000000000005, 7.200000000000005, 7.2900000000000045, 7.380000000000004, 7.470000000000004, 7.560000000000005, 7.650000000000005, 7.740000000000005, 7.830000000000005, 7.920000000000005, 8.010000000000005, 8.100000000000005, 8.190000000000005, 8.280000000000005, 8.370000000000005, 8.460000000000006, 8.550000000000006, 8.640000000000006, 8.730000000000006, 8.820000000000006, 8.910000000000005, 9}, {1.2337904625833855, 0.36603843738112785, -0.11769338887757712, -0.3681098329955359, -0.47937345149009114, -0.5099221027515239, -0.4956851295290287, -0.4584634877876244, -0.4112348238043286, -0.3615046558921315, -0.31341722318967175, -0.2690799567827693, -0.22939020966269363, -0.19454763301165873, -0.16436860245839915, -0.13847648582514377, -0.11641445147380422, -0.09771030421355482, -0.08191191150223504, -0.06860485836480235, -0.057419588115537115, -0.04803252009766394, -0.04016389498656161, -0.03357400727734647, -0.02805880470490361, -0.02344541390456177, -0.019587894403091877, -0.016363368064831095, -0.013668579842583656, -0.011416893763845028, -0.009535700215123951, -0.007964197186741762, -0.006651503241418051, -0.005555059888495783, -0.004639283533135417, -0.0038744308757724197, -0.0032356457699749376, -0.002702159659711949, -0.0022566215733179395, -0.001884537140524393, -0.0015737991839194752, -0.0013142951216224452, -0.0010975787301235865, -9.165957914671634E-4, -7.654548267266973E-4, -6.392355368414412E-4, -5.338287684710821E-4, -4.4580282911504726E-4, -3.7229182101092685E-4, -3.1090237218427683E-4, -2.596357368855036E-4, -2.1682273479414744E-4, -1.8106941430753957E-4, -1.5121167307148765E-4, -1.262773597062974E-4, -1.054546237252646E-4, -8.806548373662568E-5, -7.354375370540563E-5, -6.141660880820212E-5, -5.1289190828358516E-5, -4.2831751948311584E-5, -3.576891840885342E-5, -2.9870724503993126E-5, -2.4945125006840206E-5, -2.083174224971976E-5, -1.7396644275657192E-5, -1.452798404588796E-5, -1.2132357721322143E-5, -1.01317634471662E-5, -8.461061621119715E-6, -7.0658539530970375E-6, -5.900712259759935E-6, -4.927699324167358E-6, -4.115133660253178E-6, -3.43655796322436E-6, -2.8698776588749337E-6, -2.3966415031552594E-6, -2.001440808438576E-6, -1.6714077353745379E-6, -1.395796314767905E-6, -1.1656325575913624E-6, -9.73422260737508E-7, -8.129069946787704E-7, -6.788603280002109E-7, -5.669176538780229E-7, -4.734340776527538E-7, -3.95365738313326E-7, -3.301706997147733E-7, -2.757261845423377E-7, -2.3025945615402308E-7, -1.9229009780853246E-7, -1.6058180988447704E-7, -1.3410215560279E-7, -1.1198894456784302E-7, -9.352215957051371E-8, -7.810051258544654E-8, -6.522186662170477E-8, -5.4466885958580146E-8, -4.5485382414921765E-8, -3.79849130835389E-8, -3.23620701937668E-8},x]
y2sol(x) = DataFunction[{0, 0.09, 0.18, 0.27, 0.36, 0.45, 0.54, 0.6300000000000001, 0.72, 0.8099999999999999, 0.8999999999999999, 0.9899999999999999, 1.0799999999999998, 1.1699999999999997, 1.2599999999999998, 1.3499999999999999, 1.44, 1.53, 1.62, 1.7100000000000002, 1.8000000000000003, 1.8900000000000003, 1.9800000000000004, 2.0700000000000007, 2.1600000000000006, 2.2500000000000004, 2.3400000000000007, 2.4300000000000006, 2.520000000000001, 2.6100000000000008, 2.700000000000001, 2.790000000000001, 2.8800000000000012, 2.970000000000001, 3.0600000000000014, 3.1500000000000012, 3.2400000000000015, 3.3300000000000014, 3.4200000000000017, 3.5100000000000016, 3.600000000000002, 3.6900000000000017, 3.780000000000002, 3.870000000000002, 3.960000000000002, 4.0500000000000025, 4.140000000000002, 4.230000000000002, 4.320000000000002, 4.410000000000003, 4.500000000000002, 4.590000000000002, 4.680000000000002, 4.770000000000002, 4.860000000000002, 4.950000000000003, 5.040000000000003, 5.130000000000003, 5.220000000000002, 5.310000000000002, 5.400000000000003, 5.490000000000003, 5.580000000000003, 5.6700000000000035, 5.760000000000003, 5.850000000000003, 5.940000000000003, 6.030000000000003, 6.120000000000004, 6.2100000000000035, 6.300000000000003, 6.390000000000004, 6.480000000000004, 6.570000000000004, 6.660000000000004, 6.7500000000000036, 6.840000000000004, 6.930000000000004, 7.020000000000004, 7.110000000000005, 7.200000000000005, 7.2900000000000045, 7.380000000000004, 7.470000000000004, 7.560000000000005, 7.650000000000005, 7.740000000000005, 7.830000000000005, 7.920000000000005, 8.010000000000005, 8.100000000000005, 8.190000000000005, 8.280000000000005, 8.370000000000005, 8.460000000000006, 8.550000000000006, 8.640000000000006, 8.730000000000006, 8.820000000000006, 8.910000000000005, 9}, {3.804233948734322, 2.844781135139359, 2.164003416588986, 1.672257773105748, 1.3105287607674745, 1.0396311656071782, 0.8332774195283659, 0.673616550083822, 0.548355340180345, 0.4488937513726513, 0.36911167634817066, 0.30457490441344326, 0.25201169049137817, 0.20896465024608252, 0.17355678679700168, 0.14433225402669558, 0.12014641980289718, 0.10008874266345401, 0.08342772503358728, 0.06957090821388846, 0.058035265483144756, 0.04842489998302514, 0.040413964170770214, 0.033733379824271256, 0.028160375006795673, 0.02351014603009521, 0.019629149051119742, 0.016389660196513667, 0.013685336161025756, 0.01142757278152518, 0.009542506089045336, 0.007968534655774403, 0.006654267564297528, 0.005556821625363258, 0.0046404063093677715, 0.0038751464344810842, 0.0032361018039777367, 0.0027024502954877995, 0.0022568067988336877, 0.0018846551868423734, 0.0015738744161556397, 0.0013143430679544849, 0.0010976092868410778, 9.166152655898474E-4, 7.654672377901666E-4, 6.392434465409267E-4, 5.33833809403356E-4, 4.458060417518752E-4, 3.7229386845617226E-4, 3.1090367704106954E-4, 2.5963656848323655E-4, 2.168232647792159E-4, 1.810697520719314E-4, 1.5121188833180842E-4, 1.262774968936244E-4, 1.0545471115595273E-4, 8.806553945695695E-5, 7.354378921644417E-5, 6.141663143968172E-5, 5.1289205251584666E-5, 4.283176114034869E-5, 3.576892426701052E-5, 2.98707282374415E-5, 2.4945127386194847E-5, 2.0831743766099925E-5, 1.7396645242057153E-5, 1.4527984661781431E-5, 1.213235811383527E-5, 1.0131763697317437E-5, 8.46106178054273E-6, 7.065854054698336E-6, 5.9007123245110755E-6, 4.927699365433651E-6, 4.1151336865524275E-6, 3.436557979985021E-6, 2.869877669556597E-6, 2.396641509962741E-6, 2.00144081277702E-6, 1.6714077381394505E-6, 1.3957963165299974E-6, 1.1656325587143519E-6, 9.734222614531942E-7, 8.129069951348802E-7, 6.788603282908916E-7, 5.66917654063275E-7, 4.7343407777081554E-7, 3.9536573838856723E-7, 3.3017069976272484E-7, 2.757261845728975E-7, 2.3025945617349883E-7, 1.9229009782094446E-7, 1.6058180989238716E-7, 1.3410215560783113E-7, 1.1198894457105571E-7, 9.352215957256117E-8, 7.810051258675139E-8, 6.522186662253637E-8, 5.4466885959110124E-8, 4.548538241525952E-8, 3.798491308375414E-8, 3.236207019391101E-8},x]
parysol(x) = If[0 ≤ x ≤ t, y2sol(x)]
parxsol(x) = If[0 ≤ x ≤ t, x2sol(x)]
mixval = Min(xlist)
miyval = Min(ylist)
j = Segment((x(B), 0), B)
k = Segment((0, y(B)), B)
E = Intersect(yAxis, k)
F = Intersect(xAxis, j)
sp = 1.5 (slider from 0 to 1.5, step 0.1)
e = true
length = 0.5 (slider from 0.1 to 1.2)
l1 = Sequence(Sequence[Vector[(ii, jj), (ii, jj) + ((((2 * Min[x(D) - x(C), y(D) - y(C)])) / n * length) * UnitVector[(f(ii, jj), g(ii, jj))])], ii, x(C), x(D), H / n], jj, y(C), y(D), W / n)
ppsolb = SolveODE((-1 * g(x, y)), (-1 * f(x, y)), x(A), y(A), maxT, stepsolve)
xblist = Sequence(x(Point[ppsolb, tt]), tt, 0, 1, stepplot)
yblist = Sequence(y(Point[ppsolb, tt]), tt, 0, 1, stepplot)
tblist: (Sequence[0, 1, stepplot] * maxT)
x3sol(x) = DataFunction[{0, 0.09, 0.18, 0.27, 0.36, 0.45, 0.54, 0.6300000000000001, 0.72, 0.8099999999999999, 0.8999999999999999, 0.9899999999999999, 1.0799999999999998, 1.1699999999999997, 1.2599999999999998, 1.3499999999999999, 1.44, 1.53, 1.62, 1.7100000000000002, 1.8000000000000003, 1.8900000000000003, 1.9800000000000004, 2.0700000000000007, 2.1600000000000006, 2.2500000000000004, 2.3400000000000007, 2.4300000000000006, 2.520000000000001, 2.6100000000000008, 2.700000000000001, 2.790000000000001, 2.8800000000000012, 2.970000000000001, 3.0600000000000014, 3.1500000000000012, 3.2400000000000015, 3.3300000000000014, 3.4200000000000017, 3.5100000000000016, 3.600000000000002, 3.6900000000000017, 3.780000000000002, 3.870000000000002, 3.960000000000002, 4.0500000000000025, 4.140000000000002, 4.230000000000002, 4.320000000000002, 4.410000000000003, 4.500000000000002, 4.590000000000002, 4.680000000000002, 4.770000000000002, 4.860000000000002, 4.950000000000003, 5.040000000000003, 5.130000000000003, 5.220000000000002, 5.310000000000002, 5.400000000000003, 5.490000000000003, 5.580000000000003, 5.6700000000000035, 5.760000000000003, 5.850000000000003, 5.940000000000003, 6.030000000000003, 6.120000000000004, 6.2100000000000035, 6.300000000000003, 6.390000000000004, 6.480000000000004, 6.570000000000004, 6.660000000000004, 6.7500000000000036, 6.840000000000004, 6.930000000000004, 7.020000000000004, 7.110000000000005, 7.200000000000005, 7.2900000000000045, 7.380000000000004, 7.470000000000004, 7.560000000000005, 7.650000000000005, 7.740000000000005, 7.830000000000005, 7.920000000000005, 8.010000000000005, 8.100000000000005, 8.190000000000005, 8.280000000000005, 8.370000000000005, 8.460000000000006, 8.550000000000006, 8.640000000000006, 8.730000000000006, 8.820000000000006, 8.910000000000005, 9}, {1.2337904625833855, 2.725691868165118, 5.222596253614482, 9.327256404053506, 15.991539498337646, 26.71631275314977, 43.8653231626426, 71.15799326207149, 114.4430116985178, 182.9125884851099, 291.0082412216303, 461.41176422839624, 729.7390815208892, 1151.906244822374, 1815.688477363419, 2858.8587498828224, 4497.650575989689, 7071.420880024163, 11112.732820064648, 17457.32558730139, 27416.67151623586, 43048.73976786998, 67582.85698280213, 106086.36279463452, 166510.66729883233, 261332.63018004928, 410130.06158805604, 643622.956520909, 1010014.6152526755, 1584941.5189222025, 2487085.7067256, 3902672.1871250407, 6123907.855419635, 9609296.021063164, 1.5078275931343704E7, 2.365972159514585E7, 3.712495112942193E7, 5.825334136552148E7, 9.140601299687175E7, 1.4342599854320794E8, 2.2505069331751633E8, 3.5312812758614695E8, 5.540945109981105E8, 8.694308332352777E8, 1.3642247914278216E9, 2.1406052683295746E9, 3.358822300566411E9, 5.270323536347445E9, 8.269654303197964E9, 1.2975893666801752E10, 2.0360435189571453E10, 3.194748678818521E10, 5.0128673521490326E10, 7.86566782884762E10, 1.2341980927570233E11, 1.9365736689281107E11, 3.0386666481800977E11, 4.767953183887257E11, 7.481364143952605E11, 1.1738956532451492E12, 1.8419510523869634E12, 2.890191148001067E12, 4.534975437960969E12, 7.115791323522164E12, 1.1165324766900502E13, 1.7519407270804338E13, 2.7489532246563293E13, 4.3133548125863734E13, 6.768039917628519E13, 1.0619658027484823E14, 1.6663186136151756E14, 2.614601180108915E14, 4.1025393347268094E14, 6.437243661983525E14, 1.0100596839293776E15, 1584871366742490, 2486800212510601, 3902003607593505, 6122578071319307, 9606847378224164, 15073959541602828, 23652317164504456, 37112476661007336, 58232585876542560, 91371784984632144, 143369918206032320, 224959252884271104, 352979578199357824, 553853869146981888, 869041875193134720, 1363597225420700928, 2139594189455214592, 3357195300566272000, 5267708072779674624, 8265453514069889024, 1.2969151764670669E19, 2.034962231722536E19, 3.193015527029467E19, 5.010090882656691E19, 7.861222238939636E19, 1.1733287646981579E20},x]
y3sol(x) = DataFunction[{0, 0.09, 0.18, 0.27, 0.36, 0.45, 0.54, 0.6300000000000001, 0.72, 0.8099999999999999, 0.8999999999999999, 0.9899999999999999, 1.0799999999999998, 1.1699999999999997, 1.2599999999999998, 1.3499999999999999, 1.44, 1.53, 1.62, 1.7100000000000002, 1.8000000000000003, 1.8900000000000003, 1.9800000000000004, 2.0700000000000007, 2.1600000000000006, 2.2500000000000004, 2.3400000000000007, 2.4300000000000006, 2.520000000000001, 2.6100000000000008, 2.700000000000001, 2.790000000000001, 2.8800000000000012, 2.970000000000001, 3.0600000000000014, 3.1500000000000012, 3.2400000000000015, 3.3300000000000014, 3.4200000000000017, 3.5100000000000016, 3.600000000000002, 3.6900000000000017, 3.780000000000002, 3.870000000000002, 3.960000000000002, 4.0500000000000025, 4.140000000000002, 4.230000000000002, 4.320000000000002, 4.410000000000003, 4.500000000000002, 4.590000000000002, 4.680000000000002, 4.770000000000002, 4.860000000000002, 4.950000000000003, 5.040000000000003, 5.130000000000003, 5.220000000000002, 5.310000000000002, 5.400000000000003, 5.490000000000003, 5.580000000000003, 5.6700000000000035, 5.760000000000003, 5.850000000000003, 5.940000000000003, 6.030000000000003, 6.120000000000004, 6.2100000000000035, 6.300000000000003, 6.390000000000004, 6.480000000000004, 6.570000000000004, 6.660000000000004, 6.7500000000000036, 6.840000000000004, 6.930000000000004, 7.020000000000004, 7.110000000000005, 7.200000000000005, 7.2900000000000045, 7.380000000000004, 7.470000000000004, 7.560000000000005, 7.650000000000005, 7.740000000000005, 7.830000000000005, 7.920000000000005, 8.010000000000005, 8.100000000000005, 8.190000000000005, 8.280000000000005, 8.370000000000005, 8.460000000000006, 8.550000000000006, 8.640000000000006, 8.730000000000006, 8.820000000000006, 8.910000000000005, 9}, {3.804233948734322, 5.179554058313405, 7.181650261523744, 10.136438043301595, 14.54923553365671, 21.20566310240678, 31.32972892386143, 46.831598779767646, 70.69603416211771, 107.59148710449311, 164.82534893592953, 253.84225563091172, 392.5743920643814, 609.1285357509853, 947.5704221400522, 1476.9998323750565, 2305.7889359381907, 3603.9220408774045, 5638.046963719058, 8826.47185392249, 13825.458028377187, 21664.618911962163, 33959.37083936856, 53244.285330062645, 83496.14718227374, 130954.67919346043, 205410.33469702784, 322224.9651653468, 505502.44078912673, 793063.6605568804, 1244252.8274094115, 1952186.2574939532, 3062971.9630656573, 4805867.064770027, 7540597.731452973, 1.1831608805153515E7, 1.8564568729531214E7, 2.9129177158611964E7, 4.570600789654815E7, 7.171659331790683E7, 1.1252965037583435E8, 1.765692173104095E8, 2.770534266156496E8, 4.347228062655258E8, 6.821212445004907E8, 1.0703132302069799E9, 1.6794238385885038E9, 2.635176961873592E9, 4.134845345400367E9, 6.487968619693775E9, 1.0180243682931313E10, 1.5973774633519886E10, 2.506437416860824E10, 3.932838393853447E10, 6.170995827707945E10, 9.682874767705386E10, 1.5193340932241602E11, 2.3839775129482788E11, 3.740683174839273E11, 5.869479586856086E11, 9.20975684333203E11, 1.4450957633659417E12, 2.2674879457372803E12, 3.55789593329242E12, 5.582662708597128E12, 8.75970402475129E12, 1.3744766589510121E13, 2.156677462121996E13, 3.3840200256668023E13, 5.309829093795386E13, 8.331593163935783E13, 1.3073006015332575E14, 2.0512696811087606E14, 3.2186218474512175E14, 5.0502984393563575E14, 7.924356857313665E14, 1.2434001090814412E15, 1.9510018071809305E15, 3061289039712055, 4803423693964653, 7536979776612151, 11826158589210328, 18556238338835676, 29116292948248492, 45685892504263336, 71684959117322464, 112479626459266720, 176489789120192704, 276926934598055328, 434520937625982208, 681798612745573248, 1069797094769784832, 1678597650333641472, 2633854036450315776, 4132726757107365376, 6484575882422051840, 1.0174811158716522E19, 1.5965077635271682E19, 2.5050454413432357E19, 3.930611119487651E19, 5.866643823511721E19},x]
l = Mirror(x3sol(x), x = 0)
m = Mirror(y3sol(x), x = 0)
P2 = (-0.4683362598162746, 3.652063418039057)
P3 = (-0.06087510263909557, 3.3119622819351404)
P4 = (0.34658605453808344, 2.9718611458312236)
P5 = (0.9306720051697475, 2.6477379154503096)
P6 = (3.0991348158980814, 0.9129938655242907)
P7 = (3.5065959730752603, 0.5728927294203738)
P8 = (1.6499954214167278, 2.7070844224214623)
P9 = (3.2798400501254434, 1.3466798780057951)
ppsol2 = SolveODE(g, f, x(P2), y(P2), maxT, stepsolve)
ppsol2b = SolveODE(g, f, x(P2), y(P2), (-1 * maxT), stepsolve)
ppsol3 = SolveODE(g, f, x(P3), y(P3), maxT, stepsolve)
ppsol3b = SolveODE(g, f, x(P3), y(P3), (-1 * maxT), stepsolve)
b2 = false
b3 = false
b4 = false
b5 = false
b6 = false
b7 = false
b8 = false
b9 = false
q = 1 (slider from 1 to 10, step 1)
ppsol4 = SolveODE(g, f, x(P4), y(P4), maxT, stepsolve)
ppsol4b = SolveODE(g, f, x(P4), y(P4), (-1 * maxT), stepsolve)
ppsol5 = SolveODE(g, f, x(P5), y(P5), maxT, stepsolve)
ppsol5b = SolveODE(g, f, x(P5), y(P5), (-1 * maxT), stepsolve)
ppsol6 = SolveODE(g, f, x(P6), y(P6), maxT, stepsolve)
ppsol6b = SolveODE(g, f, x(P6), y(P6), (-1 * maxT), stepsolve)
ppsol7 = SolveODE(g, f, x(P7), y(P7), maxT, stepsolve)
ppsol7b = SolveODE(g, f, x(P7), y(P7), (-1 * maxT), stepsolve)
ppsol8 = SolveODE(g, f, x(P8), y(P8), maxT, stepsolve)
ppsol8b = SolveODE(g, f, x(P8), y(P8), (-1 * maxT), stepsolve)
ppsol9 = SolveODE(g, f, x(P9), y(P9), maxT, stepsolve)
ppsol9b = SolveODE(g, f, x(P9), y(P9), (-1 * maxT), stepsolve)