MHB -1.3.9 Verify ty'-y=t^2 is a solution of the DE

[karush]

$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$
$ty'-y=t^2\\$
$y_1(t)=3t+t^2$
\begin{align*}
t(3t+t^2)'-(3t+t^2)&=t^2\\
t(3+2t)-(3t+t^2)&=\\
3t+2t^2-3t-t^2&=\\
t^2&=t^2
\end{align*}

probably too easy

 

[HOI]

Well, learning Calculus does make some problems easy!