What is the solution for y^{''}+81y=cos(4t) ?

The solution for y^{''}+81y=cos(4t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/65 cos(4t)

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y^{''}+81y=cos(4t)

y^{^{''}} + 81 y = cos (4 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{65} cos (4 t)

Solution steps

y^{''} (t) + 81 y = cos (4 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{65} cos (4 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{65} cos (4 t)

\frac{d}{d t} (\frac{1}{3} π r (t) (t)^{2} h)

\frac{\partial}{\partial x} (\frac{7 x - 5 y}{y ^{2} + x ^{2}})

x \to - π lim ((x + π) csc (x))

8 t \frac{d y}{d t} + y = t^{7}

\frac{d}{d x} (\frac{x ^{2}}{x ^{4} + x ^{2} + 1})

What is the solution for y^{''}+81y=cos(4t) ?
The solution for y^{''}+81y=cos(4t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/65 cos(4t)