What is the solution for 4y^{''}-y=e^{x/2}+4 ?

The solution for 4y^{''}-y=e^{x/2}+4 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+(e^{x/2}x)/4-4

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4y^{''}-y=e^{x/2}+4

4 y^{^{''}} - y = e^{\frac{x}{2}} + 4

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 4

Solution steps

4 y^{''} (x) - y = e^{\frac{x}{2}} + 4

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 4

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 4

y^{^{''}} + 4 y = 3 csc (2 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{6 + e ^{x}}

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{5 + e ^{x}}

y^{^{''''}} - 4 y^{^{''}} = t^{2} + e^{t}

What is the solution for 4y^{''}-y=e^{x/2}+4 ?
The solution for 4y^{''}-y=e^{x/2}+4 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+(e^{x/2}x)/4-4