What is the solution for y^{''}+y=9x^2 ?

The solution for y^{''}+y=9x^2 is y=c_{1}cos(x)+c_{2}sin(x)+9x^2-18

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y^{''}+y=9x^2

y^{^{''}} + y = 9 x^{2}

y = c_{1} cos (x) + c_{2} sin (x) + 9 x^{2} - 18

Solution steps

y^{''} (x) + y = 9 x^{2}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 9 x^{2} - 18

y = c_{1} cos (x) + c_{2} sin (x) + 9 x^{2} - 18

y^{^{''}} - 5 y^{^{'}} + 4 y = - 3 t^{2}

y^{^{''}} - 5 y^{^{'}} = x^{2} - 2 x

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

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

y^{^{''}} + 4 y^{^{'}} = t^{2} + 2 e^{t}

What is the solution for y^{''}+y=9x^2 ?
The solution for y^{''}+y=9x^2 is y=c_{1}cos(x)+c_{2}sin(x)+9x^2-18