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Find the value(s) of the constant k for which the given function solves the associated DE:...

Find the value(s) of the constant k for which the given function solves the associated DE: y ′ +sin(2t)y=0 ; y(t)= e^kcos(2t) ; t^2 y′′+5ty′ +4y=0 ; y(t)= t^k ; Show that y(t)= c1sin(2t)+ c cos(2t) is a solution to the differential equation y′′+4y=0, where c1 and c2 are arbitrary constants.

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