What is the solution for y^{''}+16y=4e^{2t}+4sin(2t) ?

The solution for y^{''}+16y=4e^{2t}+4sin(2t) is y=c_{1}cos(4t)+c_{2}sin(4t)+1/5 e^{2t}+1/3 sin(2t)

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y^{''}+16y=4e^{2t}+4sin(2t)

y^{^{''}} + 16 y = 4 e^{2 t} + 4 sin (2 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{5} e^{2 t} + \frac{1}{3} sin (2 t)

Solution steps

y^{''} (t) + 16 y = 4 e^{2 t} + 4 sin (2 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{5} e^{2 t} + \frac{1}{3} sin (2 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{5} e^{2 t} + \frac{1}{3} sin (2 t)

x^{^{''}} + x = a cos (t)

y^{^{''}} + 36 y = 36 sec^{2} (6 x)

y^{^{'''}} + 25 y^{^{'}} = 10 sin (5 t) - 4 t^{2}

y^{^{''}} + y = 1, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + y = 4000 sec (40 x)

What is the solution for y^{''}+16y=4e^{2t}+4sin(2t) ?
The solution for y^{''}+16y=4e^{2t}+4sin(2t) is y=c_{1}cos(4t)+c_{2}sin(4t)+1/5 e^{2t}+1/3 sin(2t)