What is the solution for y^{''}+9y=cos(x) ?

The solution for y^{''}+9y=cos(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/8 cos(x)

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y^{''}+9y=cos(x)

y^{^{''}} + 9 y = cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{8} cos (x)

Solution steps

y^{''} (x) + 9 y = cos (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{8} cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{8} cos (x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 12 y = x e^{2 x}

y^{^{''}} + 3 y^{^{'}} - 4 y = (x^{3} + x) e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 3 e^{3 x} + 36 x^{2}

x^{^{''}} + 16 x = 8 sin (2 t)

y^{^{'''}} - 3 y^{^{'}} - 2 y = 2 x + 1

What is the solution for y^{''}+9y=cos(x) ?
The solution for y^{''}+9y=cos(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/8 cos(x)