What is the solution for y^{''}+25y=6sin(5x) ?

The solution for y^{''}+25y=6sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-(3xcos(5x))/5

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y^{''}+25y=6sin(5x)

y^{^{''}} + 25 y = 6 sin (5 x)

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

Solution steps

y^{''} (x) + 25 y = 6 sin (5 x)

Solve linear ODE:

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

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

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15

x^{^{'''}} + 10 x^{^{''}} + 33 x^{^{'}} + 36 x = 4 t e^{- 3 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 12 e^{t} sin (t)

y^{^{''}} + 4 y = - 16 sin (2 t)

y^{^{''}} + 4 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1

What is the solution for y^{''}+25y=6sin(5x) ?
The solution for y^{''}+25y=6sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-(3xcos(5x))/5