Question: Consider the ODE y - 2y + y = cos(4t). (a) Find the null solution yn (t). (b) Find a particular solution y, (t)

Consider the ODE y" - 2y + y = cos(4t). (a) Find

Consider the ODE y" - 2y + y = cos(4t). (a) Find the null solution yn (t). (b) Find a particular solution y, (t) by guessing that yp is of the form y(t) = M cos(4t) + N sin (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 y" - 2y + y = eit and taking the real part. Verify that you get the same answer as in (a).

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a To find the null solution we first solve the characteristic equation r2 2r 1 0 This factors as r12 ... View full answer

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