What is the solution for y^{''}+25y=sin(2x) ?

The solution for y^{''}+25y=sin(2x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1/21 sin(2x)

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y^{''}+25y=sin(2x)

y^{^{''}} + 25 y = sin (2 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{21} sin (2 x)

Solution steps

y^{''} (x) + 25 y = sin (2 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{21} sin (2 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{1}{21} sin (2 x)

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

y^{^{''}} - 5 y^{^{'}} + 7 y = 2

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 2 y = 3 e^{x} sec (x)

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

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = sin (x)

What is the solution for y^{''}+25y=sin(2x) ?
The solution for y^{''}+25y=sin(2x) is y=c_{1}cos(5x)+c_{2}sin(5x)+1/21 sin(2x)