# Solve Ay′′+By′+Cy=f(t) by Laplace Transform

Solve Ay′′+By′+Cy=f(t) by Laplace Transform
Here, ${y}_{0}={y}_{0}^{\prime }=0$ and $f\left(t\right)=n$ for ${t}_{0}
Taking the Laplace transform of both sides, I've found that
$L\left(y\right)=\frac{L\left(f\right)}{A{s}^{2}+Bs+C}$
and
$L\left(f\right)={\int }_{0}^{\mathrm{\infty }}f\left(t\right){e}^{-st}dt=\frac{n\left({e}^{-st}-{e}^{-s\left(1/n+t\right)}\right)}{s}$
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