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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.
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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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4eyyyy :) What part are you having trouble with?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4If 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
 one year ago
Best ResponseYou've already chosen the best response.0ys i know but how to solve when right having 2cos2x

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4Were 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
 one year ago
Best ResponseYou've already chosen the best response.4And 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
 one year ago
Best ResponseYou've already chosen the best response.4What do you think? :d Too confusing?
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