Given $x_1(t)$ and $x_2(t)$ two solutions of a homogeneous differential equation, what can we say about the division of those?
Is $x_1(t)/x_2(t) $ a solution of the homogeneous equation too?
I have to calculate the general solution of a non-homogeneous differential equation of order 2 ($tx''+(2-3t)x'-3x=2t^3-15t^4)$ and the only information I have is that the division of two solutions of the homogeneous differential equation is $Tan(t)$. So, how can I start?
Thank you for your time!