What is the solution for 2x^{''}+50x=cos(3t) ?

The solution for 2x^{''}+50x=cos(3t) is x=c_{1}cos(5t)+c_{2}sin(5t)+1/32 cos(3t)

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2x^{''}+50x=cos(3t)

2 x^{^{''}} + 50 x = cos (3 t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{32} cos (3 t)

Solution steps

2 x^{''} (t) + 50 x = cos (3 t)

Solve linear ODE:

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{32} cos (3 t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) + \frac{1}{32} cos (3 t)

y^{^{''}} + y = H (t) - H (t - \frac{π}{2})

y^{^{''}} + 4 y^{^{'}} + 5 y = 25 x^{2} + 13 sin (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{- 3 x} + 10 sin (x)

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 10

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = e^{x} cos (2 x)

What is the solution for 2x^{''}+50x=cos(3t) ?
The solution for 2x^{''}+50x=cos(3t) is x=c_{1}cos(5t)+c_{2}sin(5t)+1/32 cos(3t)