What is the solution for y^{''}+81y=cos(2t) ?

The solution for y^{''}+81y=cos(2t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/77 cos(2t)

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y^{''}+81y=cos(2t)

y^{^{''}} + 81 y = cos (2 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{77} cos (2 t)

Solution steps

y^{''} (t) + 81 y = cos (2 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{77} cos (2 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{77} cos (2 t)

y = \frac{3 + 4 x - 6 x}{x}

y = \frac{2}{x ^{3}}

\frac{\partial}{\partial z} (x sin (y - z))

\int \frac{x ^{3}}{u} d x

x^{3} - 3 x^{2} + 3

What is the solution for y^{''}+81y=cos(2t) ?
The solution for y^{''}+81y=cos(2t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/77 cos(2t)