What is the solution for y^{''}+25y^'=6sin(x) ?

The solution for y^{''}+25y^'=6sin(x) is y=c_{1}+c_{2}e^{-25x}-3/313 sin(x)-75/313 cos(x)

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y^{''}+25y^'=6sin(x)

y^{^{''}} + 25 y^{^{'}} = 6 sin (x)

y = c_{1} + c_{2} e^{- 25 x} - \frac{3}{313} sin (x) - \frac{75}{313} cos (x)

Solution steps

y^{''} (x) + 25 y^{'} (x) = 6 sin (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 25 x} - \frac{3}{313} sin (x) - \frac{75}{313} cos (x)

y = c_{1} + c_{2} e^{- 25 x} - \frac{3}{313} sin (x) - \frac{75}{313} cos (x)

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = \frac{e ^{x}}{x ^{3}}

y^{^{''}} - y^{^{'}} = t^{2}

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

y^{^{''}} + 2 y^{^{'}} + y = e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 9 x^{2}

What is the solution for y^{''}+25y^'=6sin(x) ?
The solution for y^{''}+25y^'=6sin(x) is y=c_{1}+c_{2}e^{-25x}-3/313 sin(x)-75/313 cos(x)