Find all real-valued solutions to the differential equation of the form x′′(t)−2x′(t)+2x(t)=f(t) with the following righ

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Find All Real Valued Solutions To The Differential Equation Of The Form X T 2x T 2x T F T With The Following Righ 1 (53.09 KiB) Viewed 32 times

Find all real-valued solutions to the differential equation of the form x′′(t)−2x′(t)+2x(t)=f(t) with the following right-hand side: (a) f(t)=cos(2t) (b) f(t)=e−tcos(2t). Hint: instead of doing variation of parameters, in each case look for a solution in a suitable form. Recall that [sin(2t)]′=2cos(2t) and [cos(2t)]′=−2sin(2t). In the case (a), also find the solution satisfying the initial conditions x(0)=0,x′(0)=0.