Why Matlab could not solve a set of linear differential equations with initial conditions through dsolve?

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Hi,
Where is the problem in my codes to solve a set of linear differential equations with initial conditions?
Any suggest?
clc
clear
ML = [2.53735261480440e-10 -1.35406667270221e-16 1.30871725825994e-18 -2.13374675288863e-15 2.03261768716403e-17 -1.61477754970584e-16 -1.62541250675724e-16;
-1.35406667270221e-16 2.53734628229043e-10 -2.73582082145325e-17 4.72489571641653e-16 1.92706132643316e-16 8.27766626176449e-16 -4.33522241607763e-16;
1.30871725825994e-18 -2.73582082145325e-17 2.53811694377620e-10 -1.38664722187494e-14 1.89471206077083e-13 -5.47669811839268e-14 2.67184290813528e-14;
-2.13374675288863e-15 4.72489571641653e-16 -1.38664722187494e-14 2.53715763347126e-10 -6.05035598297774e-15 -2.32344311157266e-14 2.96103830935012e-14;
2.03261768716403e-17 1.92706132643316e-16 1.89471206077083e-13 -6.05035598297774e-15 2.53850804700165e-10 -6.82222668978547e-14 4.82767908961758e-14;
-1.61477754970584e-16 8.27766626176449e-16 -5.47669811839268e-14 -2.32344311157266e-14 -6.82222668978547e-14 2.53705685445938e-10 3.43519159646703e-14;
-1.62541250675724e-16 -4.33522241607763e-16 2.67184290813528e-14 2.96103830935012e-14 4.82767908961758e-14 3.43519159646703e-14 2.53690028388901e-10];
KL = [6.34368385323866e-05 -5.80205835437760e-08 -1.23764005930491e-10 -1.48354797737571e-07 -3.76339592244736e-08 -1.55516201961077e-07 -2.99714848304693e-07;
-5.80205835437760e-08 0.00277423390772568 -3.64032926965371e-10 -1.15677999366471e-06 -5.05159524190059e-07 -1.14803879509422e-06 -2.36449328010142e-06;
-1.23764005930491e-10 -3.64032926965371e-10 0.00351253253565176 2.60553493225360e-07 -2.50880577858935e-05 8.96289108975872e-06 2.53253964466067e-07;
-1.48354797737571e-07 -1.15677999366471e-06 2.60553493225360e-07 0.0201021660593748 -0.000292315163965329 0.000101788069022335 -6.31134009698694e-06;
-3.76339592244736e-08 -5.05159524190059e-07 -2.50880577858935e-05 -0.000292315163965329 0.0414826409114255 0.00570625287068793 0.00236501515779697;
-1.55516201961077e-07 -1.14803879509422e-06 8.96289108975872e-06 0.000101788069022335 0.00570625287068793 0.0634851951853710 -0.000910774592712826;
-2.99714848304693e-07 -2.36449328010142e-06 2.53253964466067e-07 -6.31134009698694e-06 0.00236501515779697 -0.000910774592712826 0.121679411312940];
F=[0.000289760052925726;
0.000537710491736623;
1.24507643858810e-08;
-0.000328931258625777;
-4.51634984307082e-05;
-0.000110003762488177;
-0.000505551160254736];
syms tau_1(t) tau_2(t) tau_3(t) tau_4(t) tau_5(t) tau_6(t) tau_7(t)
v = transpose([tau_1 tau_2 tau_3 tau_4 tau_5 tau_6 tau_7]);
odes = diff(diff(v)) == -inv(ML) * KL * v;
C = [v(0) == double(0*inv(ML) * [F]) , diff(v(0)) == double(01*inv(ML) * [F])];
dsolve(odes,C)

Accepted Answer

Torsten
Torsten on 12 Nov 2022
Edited: Torsten on 12 Nov 2022
The eigenvalues of a polynomial of degree 14 (=degree of ODEs * number of ODEs) are required to get an analytical solution for your problem. But analytical formulae for roots of polynomials only exist up to degree 4.
  4 Comments
Torsten
Torsten on 12 Nov 2022
Edited: Torsten on 12 Nov 2022
ML = [2.53735261480440e-10 -1.35406667270221e-16 1.30871725825994e-18 -2.13374675288863e-15 2.03261768716403e-17 -1.61477754970584e-16 -1.62541250675724e-16;
-1.35406667270221e-16 2.53734628229043e-10 -2.73582082145325e-17 4.72489571641653e-16 1.92706132643316e-16 8.27766626176449e-16 -4.33522241607763e-16;
1.30871725825994e-18 -2.73582082145325e-17 2.53811694377620e-10 -1.38664722187494e-14 1.89471206077083e-13 -5.47669811839268e-14 2.67184290813528e-14;
-2.13374675288863e-15 4.72489571641653e-16 -1.38664722187494e-14 2.53715763347126e-10 -6.05035598297774e-15 -2.32344311157266e-14 2.96103830935012e-14;
2.03261768716403e-17 1.92706132643316e-16 1.89471206077083e-13 -6.05035598297774e-15 2.53850804700165e-10 -6.82222668978547e-14 4.82767908961758e-14;
-1.61477754970584e-16 8.27766626176449e-16 -5.47669811839268e-14 -2.32344311157266e-14 -6.82222668978547e-14 2.53705685445938e-10 3.43519159646703e-14;
-1.62541250675724e-16 -4.33522241607763e-16 2.67184290813528e-14 2.96103830935012e-14 4.82767908961758e-14 3.43519159646703e-14 2.53690028388901e-10];
KL = [6.34368385323866e-05 -5.80205835437760e-08 -1.23764005930491e-10 -1.48354797737571e-07 -3.76339592244736e-08 -1.55516201961077e-07 -2.99714848304693e-07;
-5.80205835437760e-08 0.00277423390772568 -3.64032926965371e-10 -1.15677999366471e-06 -5.05159524190059e-07 -1.14803879509422e-06 -2.36449328010142e-06;
-1.23764005930491e-10 -3.64032926965371e-10 0.00351253253565176 2.60553493225360e-07 -2.50880577858935e-05 8.96289108975872e-06 2.53253964466067e-07;
-1.48354797737571e-07 -1.15677999366471e-06 2.60553493225360e-07 0.0201021660593748 -0.000292315163965329 0.000101788069022335 -6.31134009698694e-06;
-3.76339592244736e-08 -5.05159524190059e-07 -2.50880577858935e-05 -0.000292315163965329 0.0414826409114255 0.00570625287068793 0.00236501515779697;
-1.55516201961077e-07 -1.14803879509422e-06 8.96289108975872e-06 0.000101788069022335 0.00570625287068793 0.0634851951853710 -0.000910774592712826;
-2.99714848304693e-07 -2.36449328010142e-06 2.53253964466067e-07 -6.31134009698694e-06 0.00236501515779697 -0.000910774592712826 0.121679411312940];
F=[0.000289760052925726;
0.000537710491736623;
1.24507643858810e-08;
-0.000328931258625777;
-4.51634984307082e-05;
-0.000110003762488177;
-0.000505551160254736];
ML_invers = inv(ML);
fun = @(t,v)[v(8:14);-ML_invers * KL * v(1:7)];
v0 = [0*ML_invers * F;1*ML_invers * F];
[T,V] = ode15s(fun,[0 0.015],v0);
plot(T,V(:,1))

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