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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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