Can someone show me how to do these laplace transforms of these differentials?(adsbygoogle = window.adsbygoogle || []).push({});

1) y""-4y"'+6y" -4y'+y=0

y(0)=0, y'(0)=1, y"(0)=0, y"'(0)=1

2) y"-2y'+4y=0

y(0)=2, y'(0)=0

3) y"'+2y'+y=4e^-t

y(0)=2, y'(0)=-1

4) y"-2y'+2y=cos(t)

y(0)=1, y'(0)=0

the Laplace transfrom that i got for this was

s/(s^2+a^2) * 1/(s^2-2s+2) + (s-2)/(s^2-2s+2)=y

I'm trying to find the inverse transforms of these but i have no idea how to do this because i can't factor the numerator by completing the square.

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# Homework Help: Laplace transforms

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