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+5

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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 + 5

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 + 5

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 4 x + 5

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+5