What is the solution for 2y^{''}+y^'-y=x+1 ?

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

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2y^{''}+y^'-y=x+1

2 y^{^{''}} + y^{^{'}} - y = x + 1

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

Solution steps

2 y^{''} (x) + y^{'} (x) - y = x + 1

Solve linear ODE:

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

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

x \to 3 lim (x^{2} + 4 x - 3)

\frac{d}{d x} (x^{3} - 4)

\int (1 - x)^{5} (x + 1)^{2} d x

f (x) = x^{2} + 3

\int (cos (x) + sec (x))^{2} d x

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