What is the solution for y^{''}+25y=8cos(5x) ?

The solution for y^{''}+25y=8cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(4xsin(5x))/5

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y^{''}+25y=8cos(5x)

y^{^{''}} + 25 y = 8 cos (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5}

Solution steps

y^{''} (x) + 25 y = 8 cos (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5}

y^{^{''}} - 7 y^{^{'}} + 10 y = 8 e^{x}

y^{^{''}} + a^{2} y = b cos (c x), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} - 2 y = \frac{1}{2} e^{2 t} + \frac{1}{2} e^{- 2 t}

y^{^{''}} + 5 y^{^{'}} = 29 sin (- 2 t)

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- t}, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}+25y=8cos(5x) ?
The solution for y^{''}+25y=8cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(4xsin(5x))/5