Question

 Verify that y(t) =(sint)et2 is a solution of dy =2t y+(cost)et2

Answer 1

$y(t) =e^{t^2}\sin t$

$y'(t) =(e^{t^2})'\sin t+e^{t^2}(\sin t)'=2te^{t^2}\sin t+e^{t^2}\cos t=2ty+e^{t^2}\cos t$