Find the general solution (GS) of the DE

Question

i) $(1 + t)y^{\prime} = ty+t+t^2$

ii) $y^{\prime} + \cot(t)y = 2cost$

Not sure how to start...

Answer 1

$$2) y'+\cot(t)y=2\cos(t)$$ Rewrite it as $$ y'+\frac {\cos(t)}{\sin(t)}y=2\cos(t)$$ Multiply by $\sin(t)$ $$ y'\sin(t)+\cos(t)y=2\cos(t)\sin(t)$$ $$ (y\sin(t))'=\sin(2t)$$ Integrate...

Try to do first equation on your own and post your attempt...

Members will correct it...