I have an easy question that make me crazy I have the equation :
$$ty'+2y=\sin(t)$$
I think that it's nonhomogeneous equation I use the known method to solve it but I couldn't obtain the solution that should be the right solution :
$$ {y}\mathrm{{=}}\frac{\mathrm{{-}}{t}\cos{t}\mathrm{{+}}\sin{t}\mathrm{{+}}{c}}{{t}^{2}} $$
Any explaning I will be very thankful