What is the solution for y^{''}+25y= 1/100 cos(5x) ?

The solution for y^{''}+25y= 1/100 cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(1000)

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y^{''}+25y= 1/100 cos(5x)

y^{^{''}} + 25 y = \frac{1}{100} cos (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{1000}

Solution steps

y^{''} (x) + 25 y = \frac{1}{100} cos (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{1000}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{1000}

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

\frac{d ^{2} x}{d t ^{2}} - 6 \frac{d x}{d t} - 7 x = 6

\frac{1}{6} y^{^{''}} + 6 y = 2 tan (6 t) - \frac{1}{3} e^{t}

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

y^{^{''}} + 4 y = \frac{t}{2} - \frac{t cos ( 2 t )}{2}

What is the solution for y^{''}+25y= 1/100 cos(5x) ?
The solution for y^{''}+25y= 1/100 cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(1000)