What is the solution for y^{''}-2y^'+17y=289x^2+9 ?

The solution for y^{''}-2y^'+17y=289x^2+9 is y=e^x(c_{1}cos(4x)+c_{2}sin(4x))+17x^2+4x-1

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y^{''}-2y^'+17y=289x^2+9

y^{^{''}} - 2 y^{^{'}} + 17 y = 289 x^{2} + 9

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

Solution steps

y^{''} (x) - 2 y^{'} (x) + 17 y = 289 x^{2} + 9

Solve linear ODE:

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 17 x^{2} + 4 x - 1

What is the solution for y^{''}-2y^'+17y=289x^2+9 ?
The solution for y^{''}-2y^'+17y=289x^2+9 is y=e^x(c_{1}cos(4x)+c_{2}sin(4x))+17x^2+4x-1