I have a nonhomogeneous system of differential equations I want to solve for X1(t) and X2(t) I have

Question

I have a nonhomogeneous system of differential equations: I want to solve for X1(t) and X2(t). I have

dX1/dt=X1+3X2+1 and dX2/dt=3X1+X2+1. Can I set these up in a matrix (1+3+1|0) (3+1+1|0) and use Gaussian elimination to solve?

Solutions HW 13
9.4.2 Write the given system in matrix form x0 = Ax + f
r0 (t) = 2r(t) + sin t
θ0 (t) = r(t) − θ(t) + 1 We write this as

r0 (t)
=
θ0 (t)
2
1

0
r(t)
+
−1
θ(t)

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