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## anonymous one year ago d^2y/dx^2+4dy/dx+13y=2cos2x find the complementary function and particular integral.Hence write down the full general solutions.

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1. zepdrix

eyyyy :) What part are you having trouble with?

2. 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? :)

3. anonymous

ys i know but how to solve when right having 2cos2x

4. 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. $\large\rm y_p=A\sin(2x)+B\cos(2x)$

5. 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.

6. zepdrix

What do you think? :d Too confusing?

7. anonymous

oh i knew now! thx

8. zepdrix

cool! :)

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