$$ \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=t^{3}+t^{2}+3 \begin{aligned} ext { when } t & =0 \ y & =0 \ \Delta y & (0)=0\end{aligned} \quad \begin{aligned} \frac{d y}{d t} & =1\end{aligned} $$

Question

$$ \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=t^{3}+t^{2}+3 \begin{aligned} 	ext { when } t & =0 \ y & =0 \ \Delta y & (0)=0\end{aligned} \quad \begin{aligned} \frac{d y}{d t} & =1\end{aligned} $$

Vaughn Todd · Accepted Answer

The solution to the ODE is $$ y(t) = \frac{27}{2} e^{-t} - \frac{5}{2} e^{-2t} + \frac{1}{2}t^3 - \frac{7}{4}t^2 + \frac{19}{2}t - 11 $$.

\( \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=t^{3}+t^{2}+3 \begin{aligned} \text { when } t & =0 \\ y & =0 \\ \Delta y & (0)=0\end{aligned} \quad \begin{aligned} \frac{d y}{d t} & =1\end{aligned} \)

Solución ThothAI de Upstudy

Respuesta rápida

Solución paso a paso

\( \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=t^{3}+t^{2}+3 \begin{aligned} \text { when } t & =0 \\ y & =0 \\ \Delta y & (0)=0\end{aligned} \quad \begin{aligned} \frac{d y}{d t} & =1\end{aligned} \)

Solución ThothAI de Upstudy

Respuesta rápida

Solución paso a paso

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