What is the solution for y^{''}+25y=50sin(5t) ?

The solution for y^{''}+25y=50sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)-5tcos(5t)

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y^{''}+25y=50sin(5t)

y^{^{''}} + 25 y = 50 sin (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 5 t cos (5 t)

Solution steps

y^{''} (t) + 25 y = 50 sin (5 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 5 t cos (5 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - 5 t cos (5 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = cos (2 x) - 4 sin (2 x)

y^{^{''}} + 2 y^{^{'}} + y = t^{5} e^{- 5 t}

y^{^{''}} + 16 y = 9 (t) - 9 (t - 98 π), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 8 e^{- x} + 9

y^{^{''}} + 18 y^{^{'}} + 82 y = 2 e^{- 9 x} cos (x)

What is the solution for y^{''}+25y=50sin(5t) ?
The solution for y^{''}+25y=50sin(5t) is y=c_{1}cos(5t)+c_{2}sin(5t)-5tcos(5t)