# ODE System with Variable Coefficients

hi
suppose we have this equation :

d/dt(X)=A(t)*X

x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients.
coefficients of equations and consequently A are depend on t which is time.

how i Solve this equation ?

thanks

lurflurf
Homework Helper

hi

http://arxiv.org/pdf/1011.1775v1

i can not understand how in page 5 for first example it calculate element (1,2) of I(t)(with subscript n)

can anybody help?

Last edited:
lurflurf
Homework Helper
by induction
[In(t)](1,2)=∫([A(t)](1,1)[In-1(t)](1,2)+[A(t)](1,2)[In-1(t)](2,2))dt
=∫((1)(tn-1αn-1/(n-1)!)+(t)((a t)n-1/(n-1)!))dt
and so on