What is the solution for 4y^{''}+y=cos(x) ?

The solution for 4y^{''}+y=cos(x) is y=c_{1}cos(x/2)+c_{2}sin(x/2)-1/3 cos(x)

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4y^{''}+y=cos(x)

4 y^{^{''}} + y = cos (x)

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{1}{3} cos (x)

Solution steps

4 y^{''} (x) + y = cos (x)

Solve linear ODE:

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{1}{3} cos (x)

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) - \frac{1}{3} cos (x)

What is the solution for 4y^{''}+y=cos(x) ?
The solution for 4y^{''}+y=cos(x) is y=c_{1}cos(x/2)+c_{2}sin(x/2)-1/3 cos(x)