What is the solution for (d^2y)/(dx^2)+9y=15x^2-9 ?

The solution for (d^2y)/(dx^2)+9y=15x^2-9 is y=c_{1}cos(3x)+c_{2}sin(3x)+(5x^2)/3-37/27

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(d^2y)/(dx^2)+9y=15x^2-9

\frac{d ^{2} y}{d x ^{2}} + 9 y = 15 x^{2} - 9

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5 x ^{2}}{3} - \frac{37}{27}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 y = 15 x^{2} - 9

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5 x ^{2}}{3} - \frac{37}{27}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5 x ^{2}}{3} - \frac{37}{27}

What is the solution for (d^2y)/(dx^2)+9y=15x^2-9 ?
The solution for (d^2y)/(dx^2)+9y=15x^2-9 is y=c_{1}cos(3x)+c_{2}sin(3x)+(5x^2)/3-37/27