You are Here: Home >< Maths

# 2nd order DE watch

1. Give the general solution of this DE:

d^2y/dx^2-5dy/dx+4y=3xe^x

I am able to get the complementary equation but I can't seem to finish off the question.
Because there's a 3xe^x, I have to consider a particular integral. From my 'intelligent guess' I made yp(x)=(Ax+B).e^x. But when I differentiate that and continue, my A=0 which doesn't seem right.

y=(Ax+B)e^x
y'=Axe^x+Ae^x+Be^x
y''=Axe^x+2Ae^x+Be^x
->
Axe+2Ae^x+Be^x-5Axe^x-5Ae^x-5Be^x+4Axe^x+4Be^x=3xe^x
A-5A+4A=3xe^x
0A=3xe^x.

So this could be because I have used the wrong particular integral yp(x). If this is the case, what would it be?
2. When this happens you have to multiply your original guess of particular integral by ; that is, you need to substitute . The reason why this happened is because forms part of the complimentary function, which you should have got to be . If this had happened and you'd just had, say, on the RHS, then substituting would have done the trick, but since the forcing term depends on too we need to increase the power yet further.

You don't really need to know any of what I just said; basically if you try a particular integral which is in the right form and it doesn't work, multiply the lot by x and try again. [You were right to try to start with though.]

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 6, 2011
Today on TSR

### Medicine offers

Find out which unis send them quickest

### University open days

• Sheffield Hallam University
Wed, 17 Oct '18
• Staffordshire University
Wed, 17 Oct '18
• Teesside University
Wed, 17 Oct '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams