We have an ode as such:
$y'' + (sint)y'+t^2y=0$
Also, we know that $y_1$ and $y_2$ are linearly independent solutions.
How to show that the general solution has the form: $y=c_1y_1+c_2y_2$
where $c_1,c_2$ are arbitrary constants.
It is not an ode with constant coefficients, in that case it would have $exp(rt)$ as solution. But in this case, to state the requested I would show that $y=c_1y_1+c_2y_2$ also satisfies the ode.
Is this enough to do?