Solve equation $y^{(iv)}+y=1$ with Laplace

Question

help me with this exercises,

Laplace transform $$y^{(iv)}+y=1$$ with $\ \ \ \ \ y(0)=y'(0)=y''(0)=y'''(0)=0$

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I got

$$Y(s)=\frac{1}{s(s^4+1)}$$ But, I don't know how to continue:

$s^4+1=(s^2+\sqrt2 s+1)(s^2-\sqrt2 s+1)$

help :(

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Answer 1

Hint: As you wrote, by taking Laplace from your equation, we obtained $$Y(s)=\frac{1}{s(s^4+1)}$$ Then, using partial fractions, we have $$Y(s)=\dfrac{1}{s} - \dfrac{s^3}{s^4+1}$$ Can you continue by taking inverse Laplace from this to find $y(t)$?