Laplace Transforms with IVP and linear first ODE

[Lee49645]

Homework Statement

y'' + ty' - y = 0

plugging in the known Laplace formuals i get this...
[s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0

Homework Equations

y(0) = 0
y'(0) = 3

The Attempt at a Solution

simplying to a linear first order DE
-sY'(s) + (s^2-2)Y(s) = 3

Y'(s) + [(s^2-2)/-s]Y(s) = 3

now, according to my textbook "P(x)" = [(s^2-2)/-s], and i need to find the integrating factor by integrating P(x)

use e^(p(x)) then etc.

the problem I am having is how to approach integrating p(x). i tried dividing each term by s and integrating them separately but plugging them into e causes hectic problems.

is there a different way to approach this?

 

[gabbagabbahey]

Homework Statement

y'' + ty' - y = 0

plugging in the known Laplace formuals i get this...
[s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0

I think you have an extra $-Y(s)$ in here.

now, according to my textbook "P(x)" = [(s^2-2)/-s], and i need to find the integrating factor by integrating P(x)

Ermm...you mean $P(s)$ right?

i tried dividing each term by s and integrating them separately but plugging them into e causes hectic problems.

That's the correct approach...what do you get when you do this (after correcting your 1st error)?