Question

Need help finding solution for non-homogeneous initial value problem. --See below--

Answer 1

y'' - 2y' + y = te^t + 4

iconditions; y(0) = 0; y'(0) = 0

I don't even know where to start :(
should i find general solution for homogeneous side and then find y(t) with deriv = (te^t + 4)!!

Answer 2

So three steps
1. Find the homogeneous solutions, y1 and y2 to
y'' - 2y' + y = 0
2. Find the particular solution yp to the inhomogeneous equation
3. Write down the general solution y = c1.y1 + c2.y2 + yp and substitute the initial solutions to find the final solution

Answer 3

So now, I hope step 1 is easy.

Answer 4

...easy for you. yes?

Answer 5

yes, then solve separately and add solutions?

Answer 6

yes.

Now step 2. Easiest thing here is the variation of unknown parameters.

Answer 7

Your text book should talk about this

Answer 8

The general form I'd use to substitute with this method is
yp = Ate^t + Be^t + C.

Substitute into the equation and you'll be able to solve for A, B and C.

Answer 9

Thanks. I wasn't sure which method to pursue, I'll look up the variation of parameters section.