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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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