What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=x^2+1 ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=x^2+1 is y=c_{1}e^x+c_{2}xe^x+x^2+4x+7

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(d^2y)/(dx^2)-2(dy)/(dx)+y=x^2+1

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = x^{2} + 1

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d 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^{^{''}} - 3 y^{^{'}} + 2 y = 3 e^{2 x} + 2 x

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

y^{^{''}} + 4 y = 3 sin (x) + cos (3 x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 3 - 2 x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 x + 18

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=x^2+1 ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=x^2+1 is y=c_{1}e^x+c_{2}xe^x+x^2+4x+7