• Support PF! Buy your school textbooks, materials and every day products Here!

Need help with finding particular solution to a second order differential equation

  • #1

Homework Statement


Consider the differential equation:
y''+10y'+25y= f(x)

Find a particular solution if f(x) = 32xe^(-x)

Homework Equations


I already did the general solution when f(x)=0 and that is Ae^(-5x) + Bxe^(-5x)


The Attempt at a Solution


I tried yp=axe^(-x) and got a= 4x+2 which is wrong

The answer is (2x-1)e^(-x)

does anyone know what particular solution i can try in order to get the answer?

Thanks
 

Answers and Replies

  • #2
33,070
4,771


If f(x) had been 32e-x, you would want to try yp = Ae-x. Since f(x) = 32xe-x, you want your particular solution to be yp = Ae-x + Bxe-x.

If f(x) had been 32x2e-x, you would try a particular solution of the form yp = Ae-x + Bxe-x + Cx2e-x. There's a reason for all of this, but I'll leave that for your instructor.

BTW, this is hardly a Precalculus question. You should have posted it in Calculus and Beyond.
 
  • #3


Hi, thankyou so much for your reply. I tried it and it worked!!! i shall write it down and remember that forever now!

Also, sorry about posting in the wrong section! I can't believe i did that because i took so long to check that my post was right.. i guess i forgot to check if i had clicked on the right section..! Thankyou so much though.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,769
911


Generally speaking when a "right hand side" involves an [itex]n^{th}[/itex] power of x, you should try a polynomial of degree n down.
 

Related Threads for: Need help with finding particular solution to a second order differential equation

  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
5
Views
1K
Replies
71
Views
10K
Replies
21
Views
5K
Replies
2
Views
1K
Replies
13
Views
730
Top