What is the solution for y^{''}+81y=cos(8t) ?

The solution for y^{''}+81y=cos(8t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/17 cos(8t)

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y^{''}+81y=cos(8t)

y^{^{''}} + 81 y = cos (8 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{17} cos (8 t)

Solution steps

y^{''} (t) + 81 y = cos (8 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{17} cos (8 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{17} cos (8 t)

e^{3} + 2

\int_{1}^{4} \frac{1}{x ^{2}} - \frac{8}{x ^{3}} d x

x^{^{'}} = x^{3}

\frac{1}{1 + cos ^{2} ( x )}

\int 4 x^{3} + 24 x - 1 d x

What is the solution for y^{''}+81y=cos(8t) ?
The solution for y^{''}+81y=cos(8t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/17 cos(8t)