karush
Gold Member
MHB
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$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$
$ty'-y=t^2\\$
$y_1(t)=3t+t^2$
\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
$ty'-y=t^2\\$
$y_1(t)=3t+t^2$
\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
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