What is the solution for y^{''}+y^'=2x+x ?

The solution for y^{''}+y^'=2x+x is y=c_{1}+c_{2}e^{-x}+(3x^2)/2-3x

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y^{''}+y^'=2x+x

y^{^{''}} + y^{^{'}} = 2 x + x

y = c_{1} + c_{2} e^{- x} + \frac{3 x ^{2}}{2} - 3 x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{3 x ^{2}}{2} - 3 x

y = c_{1} + c_{2} e^{- x} + \frac{3 x ^{2}}{2} - 3 x

What is the solution for y^{''}+y^'=2x+x ?
The solution for y^{''}+y^'=2x+x is y=c_{1}+c_{2}e^{-x}+(3x^2)/2-3x