Solve the IVP with Laplace Transform: begin{cases} y"+4y'+4y=(3+t)e^{-2t} y(0)=2 y'(0)=5 end{cases}

Laplace transform
asked 2020-12-21
Solve the IVP with Laplace Transform:
\(\begin{cases} y"+4y'+4y=(3+t)e^{-2t} \\ y(0)=2 \\ y'(0)=5 \end{cases}\)

Answers (1)

\(\text{Step 1}\)
\(\text{The equation is:}\)
\(\text{Now Laplace equation will be:}\)
\(\text{Step 2}\)
\(\text{Now take Laplace inverse,}\)
\(\text{By the formula of Laplace transformation the final solution will be:}\)

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