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

The solution for y^{''}+25y=cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(10)

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

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

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

2 y^{^{''}} + y^{^{'}} = x + sin (x)

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}

y^{^{''}} + 4 y = 4 cos (2 x) + 6 cos (x) + 8 x^{2} - 4 x

y^{^{''}} - 4 y^{^{'}} + 3 y = 20 cos (x)

x^{^{''}} + x^{^{'}} + 12 x = 20 cos (3 t)

What is the solution for y^{''}+25y=cos(5x) ?
The solution for y^{''}+25y=cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(10)