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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$

$ty'-y=t^2\\$

$y_1(t)=3t+t^2$

\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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