## Question

###### Consider the ODE:y" + 4y cos(wt)Where w is a positive real number. If w is a positive rational number (ie W is & number of the form for positive integers and n), and not equal to 2, show that any solution of the above ODE is periodic Hint: You 'Il find that the solution is the sum of two periodic functions with different periods; try multiple of those periods If w 2, find the general solution and show that it is unbounded as t 3 O0. In other words, if $(t) is any solution, show tha

Consider the ODE: y" + 4y cos(wt) Where w is a positive real number. If w is a positive rational number (ie W is & number of the form for positive integers and n), and not equal to 2, show that any solution of the above ODE is periodic Hint: You 'Il find that the solution is the sum of two periodic functions with different periods; try multiple of those periods If w 2, find the general solution and show that it is unbounded as t 3 O0. In other words, if $(t) is any solution, show that given any M > 0 and N > 0, YoU can find a t 2 N with |d(t)l 2 M_

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