What is the solution for y^{''}+4y^'=4x+1 ?

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

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y^{''}+4y^'=4x+1

y^{^{''}} + 4 y^{^{'}} = 4 x + 1

y = c_{1} + c_{2} e^{- 4 x} + \frac{x ^{2}}{2}

Solution steps

y^{''} (x) + 4 y^{'} (x) = 4 x + 1

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 x} + \frac{x ^{2}}{2}

y = c_{1} + c_{2} e^{- 4 x} + \frac{x ^{2}}{2}

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