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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int sec^{2} (x) + 9 d x

\int - \frac{5 ^{- x}}{ln ( 5 )} d x

\int - 36 x^{2} - 18 x - 4 d x

\int (x^{2} - 5 x + 3) d x

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{- 3 x} - e^{- x}

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