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# Find the laplace transfor?

Solve the initial value problems by the Laplace transform method

y" +2y' -3y = 0 y(0) = 1 y'(0) = 1

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- kbLv 77 years agoFavorite Answer
Apply L to both sides:

(s^2 Y(s) - 1s - 1) + 2(s Y(s) - 1) - 3 Y(s) = 0.

Solve for Y(s):

(s^2 + 2s - 3) Y(s) = s + 3

==> Y(s) = (s + 3)/(s^2 + 2s - 3)

..............= (s + 3)/((s + 3)(s - 1))

..............= 1/(s - 1).

Inverting yields y = e^t.

I hope this helps!

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