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**1. y'' -5y' + 6y = 0, y(0) = 1, y'(0) =2**

**3.**

[s^2 F(s) - s f(0) - f'(0)] -5 [F(s) - f(0)] + 6[F(s)] = 0

(s^2 +1)F(s) - (s -5)f(0) - f'(0) = 0 (s^2 + 1)F(s) - (s-5)(1) - 2 = 0

(s^2 + 1)F(s) = s -3 F(s) = (s-3)/(s^2 + 1)

Here's where I'm stuck. I can't factor the denominator to get partial fractions, so I feel like I should just divide up the fraction like this: s/(s^2 + 1) -3/(s^2 + 1) And then use cost - 3sint, but that's not the answer in my book.

[s^2 F(s) - s f(0) - f'(0)] -5 [F(s) - f(0)] + 6[F(s)] = 0

(s^2 +1)F(s) - (s -5)f(0) - f'(0) = 0 (s^2 + 1)F(s) - (s-5)(1) - 2 = 0

(s^2 + 1)F(s) = s -3 F(s) = (s-3)/(s^2 + 1)

Here's where I'm stuck. I can't factor the denominator to get partial fractions, so I feel like I should just divide up the fraction like this: s/(s^2 + 1) -3/(s^2 + 1) And then use cost - 3sint, but that's not the answer in my book.