What is the solution for y^{''}-2y^'+y=3x^2-5 ?

The solution for y^{''}-2y^'+y=3x^2-5 is y=c_{1}e^x+c_{2}xe^x+3x^2+12x+13

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y^{''}-2y^'+y=3x^2-5

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{2} - 5

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 3 x^{2} - 5

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

What is the solution for y^{''}-2y^'+y=3x^2-5 ?
The solution for y^{''}-2y^'+y=3x^2-5 is y=c_{1}e^x+c_{2}xe^x+3x^2+12x+13