What is the solution for y^{''}-2y^'+2y=5x^2-9x+5 ?

The solution for y^{''}-2y^'+2y=5x^2-9x+5 is y=e^x(c_{1}cos(x)+c_{2}sin(x))+(5x^2)/2+x/2+1/2

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y^{''}-2y^'+2y=5x^2-9x+5

y^{^{''}} - 2 y^{^{'}} + 2 y = 5 x^{2} - 9 x + 5

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

Solution steps

y^{''} (x) - 2 y^{'} (x) + 2 y = 5 x^{2} - 9 x + 5

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

What is the solution for y^{''}-2y^'+2y=5x^2-9x+5 ?
The solution for y^{''}-2y^'+2y=5x^2-9x+5 is y=e^x(c_{1}cos(x)+c_{2}sin(x))+(5x^2)/2+x/2+1/2