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2nd Order inhomogeneous ODEs

  • Thread starter andrey21
  • Start date
  • #1
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1. Using the complementary function and particular integral method find the solutio of the differential equation.

d2y/dx^2 + 3 dy/dx +2y = 20cos2x

Which satisfies y(0) = 1 y'(0) = 0



Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
201
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there are different ways to solve this differential equation.
I know you can solve it with the method of undetermined coefficients OR Variation of Parameters.
 
  • #3
466
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I have already found the complementary function to be:

y = Ae^(-t) + Be(-2t)

Im just not sure how to find the particular integral!
 
  • #4
33,173
4,858
Try yp = Ccos(2x) + Dsin(2x) for your particular solution.

Minor note: The independent variable should be x, not t, since x is the independent variable in your differential equation.
 

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