## Related questions with answers

Question

Solve the initial-value problem

$y''+5y'+4y=16x+20e^x,y(0)=0,y'(0)=3$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 12Find the homogeneous solution.

$\begin{align*} y^{\prime\prime}+5y^{\prime}+4y&= 0 \end{align*}$

$\begin{align*} \implies\\ m^2+5m+4 &= 0\\ \left(m+4\right)\left(m+1\right)&= 0\\\\ m=\left\{-4,-1\right\} \end{align*}$

$\begin{align*} \implies\\ y_c &= C_1e^{-4x}+C_2e^{-x} \end{align*}$

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