2nd order differential equation

  • #1

Homework Statement



y''+16y=3.36

This is actually part of a spring question I'm attempting at the moment, and I'm having a mental blank on how to deal with the 3.36.


Homework Equations



n/a



The Attempt at a Solution



I've found the characteristic equation and solution based from that;
[tex] c_1 cos(4x) + c_2 sin(4x) [/tex]
but the answer is
[tex] c_1 cos(4x) + c_2 sin(4x) + 0.21 [/tex]
 
Last edited:

Answers and Replies

  • #2
SteamKing
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Remember: The general solution to any linear non-homogeneous differential eq. is equal to the soln. to the homogeneous sq. plus the particular soln. to the non-homogeneous eq.
What is your characteristic eq. here?
 
  • #3
vela
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You found the homogeneous solution. You need to find the particular solution. Try substituting a trial solution of the form yp=A and solving for A.
 
  • #4
You found the homogeneous solution. You need to find the particular solution. Try substituting a trial solution of the form yp=A and solving for A.

[tex] y_p = A [tex]
so doing that I get A = 0.21, which gives me the correct solution.

thanks.
 
  • #5
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However do you know the rationale for choosing trail function as A instead of A x
 
  • #6
yep. so it isn't a multiple of the homogenous solution. I did a course of DE's a while ago, I just forgot what to do in this case.
 
  • #7
HallsofIvy
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However do you know the rationale for choosing trail function as A instead of A x
If you had tried Ax, then (Ax)''= 0 so the equation would have been 16Ax= 3.36. The left side has an "x" and the right side doesn't. May I ask why you are doing this problem? I would imagine it is because you are taking a course in differential equations but I cannot imagine you having a homework problem like this if you are not in a chapter of your textbook that has a detailed description of "Undetermined Coefficients" as this method is called.
 

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