What is the solution for y^{''}+25y=cos(8t) ?

The solution for y^{''}+25y=cos(8t) is y=c_{1}cos(5t)+c_{2}sin(5t)-1/39 cos(8t)

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y^{''}+25y=cos(8t)

y^{^{''}} + 25 y = cos (8 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{39} cos (8 t)

Solution steps

y^{''} (t) + 25 y = cos (8 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{39} cos (8 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{39} cos (8 t)

\frac{d}{d x} (\frac{3 x ^{- 2} + 2}{x ^{2} + 8})

\frac{d}{d x} (- \frac{- 2 ln ( x ) + 3}{x ^{3}})

\frac{( 12 s + 3 )}{s ^{2} ( 2 s + 8 )}

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

y^{^{'}} + \frac{y}{9.33} = 6.429

What is the solution for y^{''}+25y=cos(8t) ?
The solution for y^{''}+25y=cos(8t) is y=c_{1}cos(5t)+c_{2}sin(5t)-1/39 cos(8t)