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

The solution for y^{''}+25y=6sin(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1/4 sin(x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2 x} (cos (x) - 8 sin (x))

4 y^{^{''}} - 8 y^{^{'}} + 8 y = e^{x} sec (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{e ^{x} + 1}

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{x ^{2} + 1}

What is the solution for y^{''}+25y=6sin(x) ?
The solution for y^{''}+25y=6sin(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1/4 sin(x)