Question $5$

$5.$ If

$10$ pts

$y^{\text{'}\text{'}}+4y^{\text{'}}+5y=e^{-t}(cost+3sint).,y(0)=0,$ and $y^{\text{'}}(0)=4$

then $y((\frac{}{2}))=?$

then $y((\frac{}{2}))=?$

Note: $e^{-t}(cost+3sint)$ is e raised to the power $-t$ and the result is multiplies by $($cos $t+3sint$

$0\mathrm{.}37045$

None of the other answers

$0\mathrm{.}41576,$

$0\mathrm{.}25109,$

$0\mathrm{.}38074$