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

What exactly do they want?

  • #1
1,010
1

Homework Statement



Set up but do not solve for the appropriate particular solution yp for the differential equation

y''+25y=–1xcos(5x)

using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).

In your answer, give undetermined coefficients as A, B, etc.

Homework Equations


Possible Derivatives
  • sin(x)
  • cos(x)
  • xsin(x)
  • xcos(x)



The Attempt at a Solution



This seems like the solution should simply be

[tex] A*x*sin(5*x)+B*x*cos(5*x)+C*cos(5*x)+D*sin(5*x) [/tex]
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,808
933
What solution are you talking about? The problem said "Set up but do not solve for the appropriate particular solution yp for the differential equation
y''+25y=–1xcos(5x)
using the Method of Undetermined Coefficients"

Normally, to get a solution of the form "x cos(5x)" you would use (Ax+B) cos(5x)+ (Cx+ D) sin(5x). However, in this case cos(5x) and sin(5x) are solutions to the homogeneous equation. Multiply what you would normally use by x: (Ax2+ Bx)cos(5x)+ (Cx2+ Dx)sin(5x).
 

Related Threads on What exactly do they want?

Replies
3
Views
2K
Replies
10
Views
60K
  • Last Post
Replies
5
Views
1K
Replies
8
Views
615
  • Last Post
Replies
1
Views
854
Replies
25
Views
3K
  • Last Post
Replies
10
Views
3K
Top