MHB Did I Apply Laplace Transforms Correctly?

[shamieh]

Solev by Laplace Transforms

$y'' - 5y' + 6y = 1$ $y(0) = 1$, $y'(0) = 0$So I am getting stuck. Here's my work

$s^2Y - 5sY + 6Y = \frac{1}{s} + s - 5$

multiplied through by $s$ to get

$s^3Y - 5s^2Y + 6sY = 1 + s^2 - 5s$

so:

$Y = \frac{1+s^2-5s}{s^3-5s^2+6s}$

so: $1+s^2-5s = \frac{A}{s} + \frac{B}{s-2} + \frac{C}{s-3}$

so: is it correct to say $1+s^2-5s = A(s-2)(s-3) + Bs(s-3) + Cs(s-2)$

 

[shamieh]

snvm i figured it out lol