What is the solution for y^{''}+3y=cos(x) ?

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

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y^{''}+3y=cos(x)

y^{^{''}} + 3 y = cos (x)

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

Solution steps

y^{''} (x) + 3 y = cos (x)

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 2 x \cdot cos (5 x)

y^{^{''''}} + 2 y^{^{''}} + y = cos (3 x) + 5

y^{^{''}} - y^{^{'}} - 2 y = x, y (0) = 1, y^{^{'}} (0) = 0

x^{^{''}} - 2 x^{^{'}} - 3 x = e^{4 t}

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = - 2 e^{x} - 3 x

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