# Solve equation y^((iv))+y=1 with Laplace

Solve equation ${y}^{\left(iv\right)}+y=1$ with Laplace
with
I got
$Y\left(s\right)=\frac{1}{s\left({s}^{4}+1\right)}$
But, I don't know how to continue:
${s}^{4}+1=\left({s}^{2}+\sqrt{2}s+1\right)\left({s}^{2}-\sqrt{2}s+1\right)$
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Kenley Rasmussen
Hint: As you wrote, by taking Laplace from your equation, we obtained
$Y\left(s\right)=\frac{1}{s\left({s}^{4}+1\right)}$
Then, using partial fractions, we have
$Y\left(s\right)=\frac{1}{s}-\frac{{s}^{3}}{{s}^{4}+1}$