What is the solution for y^{''}+9y=18x^2+9x-6 ?

The solution for y^{''}+9y=18x^2+9x-6 is y=c_{1}cos(3x)+c_{2}sin(3x)+2x^2+x-10/9

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y^{''}+9y=18x^2+9x-6

y^{^{''}} + 9 y = 18 x^{2} + 9 x - 6

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x^{2} + x - \frac{10}{9}

Solution steps

y^{''} (x) + 9 y = 18 x^{2} + 9 x - 6

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x^{2} + x - \frac{10}{9}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 2 x^{2} + x - \frac{10}{9}

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

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

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 x e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x

y^{^{''}} - 9 y = sinh (3 x)

What is the solution for y^{''}+9y=18x^2+9x-6 ?
The solution for y^{''}+9y=18x^2+9x-6 is y=c_{1}cos(3x)+c_{2}sin(3x)+2x^2+x-10/9