What is the solution for y^{''}+y^'-2y=e^x+2 ?

The solution for y^{''}+y^'-2y=e^x+2 is y=c_{1}e^x+c_{2}e^{-2x}+(e^xx)/3-1

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y^{''}+y^'-2y=e^x+2

y^{^{''}} + y^{^{'}} - 2 y = e^{x} + 2

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{e ^{x} x}{3} - 1

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = e^{x} + 2

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{e ^{x} x}{3} - 1

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{e ^{x} x}{3} - 1

What is the solution for y^{''}+y^'-2y=e^x+2 ?
The solution for y^{''}+y^'-2y=e^x+2 is y=c_{1}e^x+c_{2}e^{-2x}+(e^xx)/3-1