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

The solution for y^{''}+2y^'=2x+4 is y=c_{1}+c_{2}e^{-2x}+(x^2)/2+(3x)/2

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y^{''}+2y^'=2x+4

y^{^{''}} + 2 y^{^{'}} = 2 x + 4

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

Solution steps

y^{''} (x) + 2 y^{'} (x) = 2 x + 4

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'=2x+4 ?
The solution for y^{''}+2y^'=2x+4 is y=c_{1}+c_{2}e^{-2x}+(x^2)/2+(3x)/2