Question

Solve the initial problem
\[y_1''=2y_1+y_2+y_1'+y_2'\]\[y_2''=-5y_1+2y_2+5y_1'-y_2'\]\(y_1(0)=y_2(0)=y_1'(0)=4\), \(y_2'(0)=-4\)

Answer 1

Integrate.

Answer 2

Note that I put this under linear algebra.

Answer 3

I think it has something to do with eigenvalues and eigenvectors

Answer 4

and diagonalization too

Answer 5

let y'1 = u, and y'2 = v, you get 4x4 system.

Answer 6

Hmm.. How??