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

The solution for 4y^{''}-y=e^{x/2}+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^{x/2}+7

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

y^{^{''}} + 6 y^{^{'}} + 13 y = e^{- 3 x} cos (2 x)

y^{^{''}} + y^{^{'}} - 6 y = 2 x^{2} + 1

y^{^{''}} + 4 y = 3 sin (3 t)

y^{^{''}} + 9 y = cos (x) + \frac{1}{3} cos (3 x)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} sec^{3} (x)

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