# What exactly do they want?

1. Mar 2, 2007

### 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).

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

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

2. Mar 2, 2007

### HallsofIvy

Staff Emeritus
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).