Help with particular integrals

SoSolid

SoSolid

SoSolid

Associate
Joined
28 Jul 2003
Posts
1,987
Location
The Moon
I am stuck solving this second order differential equation:

2y" -y' -3y = 10xe^-x


I can easily find the complimentary function. The problem is that the x on the RHS mucks everything up, I do not know which standard format to use to solve for the particular integral. Can someone please advise me on just this part.
 
Hey yeh I had originally tried the first method suggested. The thing is, how do you know which is the correct method to substitute in. I mean if I am in an exam I do not want to be messing around trying to get the correct format to use. Any hints / tips on how to do this?
 
Psiko said:
Your solution is composed of a complimentary function and a particular integral. The point of the complimentary function is that the LHS of your differential equation, in this case 2y" -y' -3y, annihilates it, ie. takes it to zero. Then, your particular integral is the part that provides the RHS of the differential equation. So when you put your particular integral y, into 2y" -y' -3y, you must get 10xe^-x. So, you are putting y = your particular integral into 2y" -y' -3y, and you want to get 10xe^-x.

So to find the PI, we can just put y = (ax+bx^2)e^-x (my previous post contains a mistake, which I will edit) into 2y" -y' -3y. Then compare this result to 10xe^-x and you should be able to match up coefficients of xe^-x and x^2 e^-x and possibly e^-x to find out what a and b are.

I hope that helps.
Click to expand...

Hey yeh that helps thanks, I am just tired and being slow. It makes sense about substituting the answer back in and seeing if it is correct. I will give it a whirl.
 
You must log in or register to reply here.
Back
Top Bottom