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

The solution for y^{''}+9y=x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+(x^2)/9-2/81

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

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

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x ^{2}}{9} - \frac{2}{81}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x ^{2}}{9} - \frac{2}{81}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{x ^{2}}{9} - \frac{2}{81}

What is the solution for y^{''}+9y=x^2 ?
The solution for y^{''}+9y=x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+(x^2)/9-2/81