What is the solution for 4y^{''}-y=e^{1/2 x}+7 ?

The solution for 4y^{''}-y=e^{1/2 x}+7 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+(e^{x/2}x)/4-7

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4y^{''}-y=e^{1/2 x}+7

4 y^{^{''}} - y = e^{\frac{1}{2} x} + 7

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 7

Solution steps

4 y^{''} (x) - y = e^{\frac{1}{2} x} + 7

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 7

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{4} - 7

What is the solution for 4y^{''}-y=e^{1/2 x}+7 ?
The solution for 4y^{''}-y=e^{1/2 x}+7 is y=c_{1}e^{x/2}+c_{2}e^{-x/2}+(e^{x/2}x)/4-7