What is the solution for y^{''}-2y^'+y=x^2+1 ?

The solution for y^{''}-2y^'+y=x^2+1 is y=c_{1}e^x+c_{2}xe^x+x^2+4x+7

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y^{''}-2y^'+y=x^2+1

y^{^{''}} - 2 y^{^{'}} + y = x^{2} + 1

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 4 x + 7

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = x^{2} + 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 4 x + 7

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 4 x + 7

y^{^{''}} - 2 y^{^{'}} + y = \frac{3 e ^{t}}{1 + t ^{2}}

y^{^{''}} + y = 4 x + 10 sin (x), y (π) = 0, y^{^{'}} (π) = 2

9 y^{^{''}} - 6 y^{^{'}} + y = cos (t)

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

y^{^{''}} - y = c^{x} + 2 c^{2 x}

What is the solution for y^{''}-2y^'+y=x^2+1 ?
The solution for y^{''}-2y^'+y=x^2+1 is y=c_{1}e^x+c_{2}xe^x+x^2+4x+7