What is the solution for y^{''}+y=cos(0.9x) ?

The solution for y^{''}+y=cos(0.9x) is y=c_{1}cos(x)+c_{2}sin(x)+5.26315…cos(0.9x)

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y^{''}+y=cos(0.9x)

y^{^{''}} + y = cos (0.9 x)

y = c_{1} cos (x) + c_{2} sin (x) + 5.26315 \dots cos (0.9 x)

Solution steps

y^{''} (x) + y = cos (0.9 x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 5.26315 \dots cos (0.9 x)

y = c_{1} cos (x) + c_{2} sin (x) + 5.26315 \dots cos (0.9 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 x e^{2 x} + 10 sin (2 x)

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

y^{^{''}} + (- 8) y^{^{'}} + 20 y = 100 x^{2} - 65 x e^{x}

y^{^{''}} - 2 y^{^{'}} + y = 6 x e^{x} + 4 e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 4

What is the solution for y^{''}+y=cos(0.9x) ?
The solution for y^{''}+y=cos(0.9x) is y=c_{1}cos(x)+c_{2}sin(x)+5.26315…cos(0.9x)