Solve the system of differential equations $\frac{dx}{dt}+\frac{-4x+2y}t=-9, \frac{dy}{dt}+\frac{x-5y}t=3$ 
Solve the system of differential equations
  $$\frac{dx}{dt}+\frac{-4x+2y}t=-9$$ $$\frac{dy}{dt}+\frac{x-5y}t=3$$
  in $t\ge 1$ subject to $x=0$ and $y=0$ at $t=1$.

It gives the hint
[powers of
$t$].
I have tried rearranging, differentiating and from the hint I thought to try series solution but nothing works.
Thank you for any help

Considering the following linear combinations:
$$\frac{dx}{dt}+\frac{dy}{dt}-\frac{3(x+y)}{t}+6=0$$
$$\frac{dx}{dt}-2\frac{dy}{dt}-\frac{6(x-2y)}{t}+15=0$$
Can you proceed?
