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**[SOLVED] Laplace Transform (Should be easy)**

**1. Homework Statement**

I know there are other ways to solve this, but I HAVE to use Laplace Transform

y''-y'-6y=0 where y(0)=2 and y'(0)=-1

**3. The Attempt at a Solution**

Written as Laplace:

y''-y'-6y=0

[tex]\Rightarrow s^2*Y(s)-s*y(0)-y'(0)-s*Y(s)+y(0)-6*Y(s)=0[/tex]

[tex]\Rightarrow s^2*Y(s)-2s+1-s*Y(s)+2-Y(s)=0[/tex]

[tex]\Rightarrow s^2*Y(s)-s*Y(s)-Y(s)=-3+2s[/tex]

[tex]\Rightarow Y(s)=\frac{-3+2s}{s^2-s-1}[/tex]

Am I missing something? The numerator and denominator don't factor. Is a separation by partial fractions my next step? Or did I miss something that would make it way easier?

Thanks