What exactly do they want?

[Tom McCurdy]

1. The problem statement, all variables and given/known data

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.
2. Relevant equations
Possible Derivatives

sin(x)
cos(x)
xsin(x)
xcos(x)




3. The attempt at a solution

This seems like the solution should simply be

A*x*sin(5*x)+B*x*cos(5*x)+C*cos(5*x)+D*sin(5*x)

[HallsofIvy]

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).