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2. Consider the ODE y2y+y=cos(4t) (a) Find the null solution yn(t). (b) Find a particular solution yp(t) by guessing that yp is of the form

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2. Consider the ODE y2y+y=cos(4t) (a) Find the null solution yn(t). (b) Find a particular solution yp(t) by guessing that yp is of the form yp(t)=Mcos(4t)+ Nsin(4t), plugging the guess into the equation, and solving for M and N. (Method of Undetermined Coefficients.) (c) Find a particular solution by finding a particular solution to y2y+y=e4it and taking the real part. Verify that you get the same answer as in (a)

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