# Question about ordinary differential equations

Considering the differential equation

$$y'(x) = A y(x) + g(x) e^{ax}$$

where $$A in Bbb R^{2 times 2}$$ and $$a$$ is no eigenvalue of $$A$$, and $$g(x)$$ a polynomial vector, then there exists a particular solution

$$y_p(x) = h(x) e^{ax}$$

where $$h(x)$$ is a polynomial vector.

I tried some approaches, but I couldn’t solve it.