What is the solution for (d^2y)/(dx^2)+4y=cos(9/4 x) ?

The solution for (d^2y)/(dx^2)+4y=cos(9/4 x) is y=c_{1}cos(2x)+c_{2}sin(2x)-16/17 cos((9x)/4)

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(d^2y)/(dx^2)+4y=cos(9/4 x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (\frac{9}{4} x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{16}{17} cos (\frac{9 x}{4})

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (\frac{9}{4} x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{16}{17} cos (\frac{9 x}{4})

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{16}{17} cos (\frac{9 x}{4})

What is the solution for (d^2y)/(dx^2)+4y=cos(9/4 x) ?
The solution for (d^2y)/(dx^2)+4y=cos(9/4 x) is y=c_{1}cos(2x)+c_{2}sin(2x)-16/17 cos((9x)/4)