[John taylor]

By considering a particular solution of the form (a,b) + (c,d)t, find the general solution to the following, satisfying initial conditions x(0)=1,y(0)=1.
dx/dt = 17x - 54y + 53 + 125t , dy/dt = 9x - 28y + 30 + 65t

I found the complemetary function to be Ae^(-10*t)*(2,1) + B*e^(-t)*(3,1).
However, i don't know how to find the particular solution....


Thanks
Note: (a,b) and so on represent column vectors.

[Allofthem]

Yo, well they've told you what to try right? (x,y) = (a,b) + (c,d)t, so (1,1) = (a,b) + (c,d) * 0 for a start.
(x,y) = (1,1) + (c,d)t.

I've not done the question but next you'll want to differentiate (x,y) wrt. t and you get (dx/dt, dy/dt), compare this to what you're given and so on.