# I am stuck with this equation. If you can help me y''(t) + 12 y'(t) + 32 y(t) = 32 u(t) wi

I am stuck with this equation. If you can help me
$y{}^{″}\left(t\right)+12{y}^{\prime }\left(t\right)+32y\left(t\right)=32u\left(t\right)$ with $y\left(0\right)={y}^{\prime }\left(0\right)=0$
I found the laplace transform for y(t)
$Y\left(p\right)=x=\frac{32}{\left(p\left({p}^{2}+12p+32\right)\right)}$
so i need the laplace transform of y(t) and then the solution for y(t).
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jeffster830gyz
$\frac{32}{p\left({p}^{2}+12p+32\right)}=\frac{32}{p\left({\left(p+6\right)}^{2}-{2}^{2}\right)}=\frac{32}{p\left(p+4\right)\left(p+8\right)}$
Now use partial fractions method to get
$\frac{a}{p}+\frac{b}{p+4}+\frac{c}{p+8}$
Then the Laplace inverse would be,
$a+{b}^{-4t}+{c}^{-8t}$