I solved the differential equation by eigenvalue​s/eigenvec​tors, how would I solve for the constants from my initial conditions?

syms lambda

A = [-8/3 0 0; 8/3 -8/2 0; 0 8/2 -8/24];

Id3 = sym([1,0,0;0,1,0;0,0,1])

B = lambda*Id3-A

evs = solve(p)

null(evs(1)*Id3-A)

[evctrs,d] = eig(A)

x0 = [3; 7; 6];

lambda_1 = d(1,1);

lambda_2 = d(2,2);

lambda_3 = d(3,3);

vec_1 = evctrs(:,1);

vec_2 = evctrs(:,2);

vec_3 = evctrs(:,3);

syms C1 C2 C3 t

X = C1*vec_1*exp(-lambda_1*t)+C2*vec_2*exp(-lambda_2*t)+C3*vec_3*exp(-lambda_3*t)

% I have initial conditions x1(0)=3, x2(0)=7, and x3(0)=6, but I am not sure how I would equate them to solve for the constants in my equation.

Answer 1

[Navya Seelam]

Hi,

You can use vpasolve to solve for C1, C2, C3. Try the following

vpasolve(subs(X(1),t,0)==3,C3) % to solve for C3.

Similarly you can solve for C2 and C3.