What is the solution for y^{''}+25y=24sin(t) ?

The solution for y^{''}+25y=24sin(t) is y=c_{1}cos(5t)+c_{2}sin(5t)+sin(t)

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y^{''}+25y=24sin(t)

y^{^{''}} + 25 y = 24 sin (t)

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

Solution steps

y^{''} (t) + 25 y = 24 sin (t)

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} = 1 - 2 e^{3 x}

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

y^{^{''}} + y^{^{'}} + y = x + cos (x)

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

y^{^{''''}} - y = 14 t + cos (t)

What is the solution for y^{''}+25y=24sin(t) ?
The solution for y^{''}+25y=24sin(t) is y=c_{1}cos(5t)+c_{2}sin(5t)+sin(t)