What exactly do they want?

  • #1
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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
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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).
 

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