What is the solution for y^{''}+y^'=x,y(0)=8,y^'(0)=0 ?

The solution for y^{''}+y^'=x,y(0)=8,y^'(0)=0 is y=(x^2)/2-x-e^{-x}+9

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y^{''}+y^'=x,y(0)=8,y^'(0)=0

y^{^{''}} + y^{^{'}} = x, y (0) = 8, y^{^{'}} (0) = 0

y = \frac{x ^{2}}{2} - x - e^{- x} + 9

Solution steps

y^{''} (x) + y^{'} (x) = x

Solve linear ODE:

y = \frac{x ^{2}}{2} - x - e^{- x} + 9

y = \frac{x ^{2}}{2} - x - e^{- x} + 9

What is the solution for y^{''}+y^'=x,y(0)=8,y^'(0)=0 ?
The solution for y^{''}+y^'=x,y(0)=8,y^'(0)=0 is y=(x^2)/2-x-e^{-x}+9