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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int \frac{( x + 7 ) ^{5}}{x} d x

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

\frac{\partial}{\partial z} ((x + z) e^{x - y})

\int \frac{1}{9 e ^{- 2 x} + e ^{2 x}} d x

\frac{d}{d x} (ln (sinh (4 x)))

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