I need to make a matlab program to find the solutions for 0<=t<=1 for
x1'(x) = 2x1 -3x2 +4x3 +0x4 -2x5 -2, x1(0)=1
x2'(x) = x1 - 2x2 - 2x3 +x4 +2x5 -1, x2(0)=-1
x3'(x) = 2x1 + 4x2 +3x3 +x4 -x5 -2, x3(0)=1
x4'(x)=-2x1 +0x2 +x3 + 4x4 -3x5 +1, x4(0)=2
x5'(x)=0x1 -x2 +2x3 -3x4 -2x5 +1, x5(0)=3
and I made a program, and I got an output:
w(1)= 94.70989959 w(2)= -5.06974461 w(3)= 81.70881908 w(4)= 7.03658123 w(5)= 12.84918264
but I have no idea how to tell whether or not I'm right. The other examples I've done have been higher order initial value problems that depended on t... so I used the same kind of scheme... but this one doesn't seem to depend on t... so I'm not sure if I'm suppose to do something different or not?
Is there a way to get an exact solution for this for me to check to see if I'm right or?