What is the solution for y^{''}+8y^'+25y=10sin(5t)-25 ?

The solution for y^{''}+8y^'+25y=10sin(5t)-25 is y=e^{-4t}(c_{1}cos(3t)+c_{2}sin(3t))-1/4 cos(5t)-1

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y^{''}+8y^'+25y=10sin(5t)-25

y^{^{''}} + 8 y^{^{'}} + 25 y = 10 sin (5 t) - 25

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

Solution steps

y^{''} (t) + 8 y^{'} (t) + 25 y = 10 sin (5 t) - 25

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 24 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)

What is the solution for y^{''}+8y^'+25y=10sin(5t)-25 ?
The solution for y^{''}+8y^'+25y=10sin(5t)-25 is y=e^{-4t}(c_{1}cos(3t)+c_{2}sin(3t))-1/4 cos(5t)-1