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

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

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

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

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

Solution steps

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

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

y^{^{''}} + y^{^{'}} = tan (t)

x^{^{''}} - 2 x^{^{'}} + 2 x = t

y^{^{''}} - 4 y^{^{'}} - 2 y = 2 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 7

y^{^{''}} + 4 y^{^{'}} + 12 y = 4 x^{2}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 9 e^{3 x}

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