anonymous
  • anonymous
d^2y/dx^2+4dy/dx+13y=2cos2x find the complementary function and particular integral.Hence write down the full general solutions.
Mathematics
katieb
  • katieb
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zepdrix
  • zepdrix
eyyyy :) What part are you having trouble with?
zepdrix
  • zepdrix
If we look for just the solutions to the homogeneous first,\[\large\rm y''+4y'+13y=0\]We get a characteristic equation that looks like this,\[\large\rm r^2+4r+13=0\]Understand that part? :)
anonymous
  • anonymous
ys i know but how to solve when right having 2cos2x

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zepdrix
  • zepdrix
Were you able to find the homogeneous solution? It should give you something like this:\[\large\rm y_h=c_1e^{-2x}\cos(3x)+c_2e^{-2x}\sin(3x)\]Then to find the particular solution, we assume that it has the form of the right side, more generally though, sines and cosines. \[\large\rm y_p=A\sin(2x)+B\cos(2x)\]
zepdrix
  • zepdrix
And then we take a couple derivatives to find our \(\large\rm y'_p\) and \(\large\rm y''_p\) and then plug all of that back into the orginal differential equation.
zepdrix
  • zepdrix
What do you think? :d Too confusing?
anonymous
  • anonymous
oh i knew now! thx
zepdrix
  • zepdrix
cool! :)

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