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}

y^{^{''}} - 2 y^{^{'}} + y = \frac{11 e ^{t}}{1 + t ^{2}}

(D^{2} + 4) y = sin (2 x)

y^{^{''}} - 5 y^{^{'}} + 6 y = 6 x + 2 - 3 e^{2 x}

y^{^{'''}} - 4 y^{^{''}} + 6 y^{^{'}} - 4 y = x + e^{x} cos (x)

y^{^{''}} + 16 y = 9 sec (4 x)

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