-) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of undtermined coefficients.

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: Find the solution(s) of the equation sin (x + 1) = v2 cos e within the interval 0 < x < 27.

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Q: Determine the form to be used for x when using the method of undetermined coefficients. x" + 2x = 8…

A: Given DE is  x"+2x=8sin(2t) ......(1)

Q: 1) Solve for r, 0 <x< 2n. sin (4x) – sin (2x) = 0

A: Given that: sin(4x)-sin(2x)=0              and             0≤x≤2π

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…