Give the general solution of this DE:
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.
So this could be because I have used the wrong particular integral yp(x). If this is the case, what would it be?
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2nd order DE watch
- Thread Starter
- 06-04-2011 15:40
- 06-04-2011 15:46
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.]