What is the solution for 2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0 ?

The solution for 2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0 is y=(-5/3+7)e^{x/2}+5/3 e^{-x}-x-6

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2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0

2 y^{^{''}} + y^{^{'}} - y = x + 5, y (0) = 1, y^{^{'}} (0) = 0

y = (- \frac{5}{3} + 7) e^{\frac{x}{2}} + \frac{5}{3} e^{- x} - x - 6

Solution steps

2 y^{''} (x) + y^{'} (x) - y = x + 5

Solve linear ODE:

y = (- \frac{5}{3} + 7) e^{\frac{x}{2}} + \frac{5}{3} e^{- x} - x - 6

y = (- \frac{5}{3} + 7) e^{\frac{x}{2}} + \frac{5}{3} e^{- x} - x - 6

What is the solution for 2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0 ?
The solution for 2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0 is y=(-5/3+7)e^{x/2}+5/3 e^{-x}-x-6