What is the solution for y^{''}+2y^'+y=3x+8 ?

The solution for y^{''}+2y^'+y=3x+8 is y=c_{1}e^{-x}+c_{2}xe^{-x}+3x+2

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y^{''}+2y^'+y=3x+8

y^{^{''}} + 2 y^{^{'}} + y = 3 x + 8

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

Solution steps

y^{''} (x) + 2 y^{'} (x) + y = 3 x + 8

Solve linear ODE:

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

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

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\int \frac{1}{1 + 9 x ^{2}} d x

What is the solution for y^{''}+2y^'+y=3x+8 ?
The solution for y^{''}+2y^'+y=3x+8 is y=c_{1}e^{-x}+c_{2}xe^{-x}+3x+2