How to Find the Laplace Transform of an Unknown Solution Function?

[Lucy77]

This one has me stumped


Find the Laplace Transform of the unknown solution function for the following initial value problem:

y'' + 4y' - 5y = te^t, y(0)=1, y'(0)= 0

(Do Not actually find the function, only its transform. Then, without carrying out the steps, indiacate briefly how you would proceed to find the unknown solution function.)

Thanks

 

[faust9]

As with your other question, Laplace transforms are linear thus you can do each elemnt individually. What have you done thus far?

 

[faust9]

Also, $L \{ y^{(n)} \}$

where n is the derivative is

$$s^nY(s)-s^{n-1}y^{(n-1)}(0)-s^{n-2}y^{(n-2)}(0)-...-y(0)$$

PS. click on the equation to see how to use LaTex extensions. A little popup box should appear with a "click to read LaTex guide" at the bottom.

Good luck.