What is the solution for (d^2y)/(dx^2)+(dy)/(dx)=x+e^{-3x} ?

The solution for (d^2y)/(dx^2)+(dy)/(dx)=x+e^{-3x} is y=c_{1}+c_{2}e^{-x}+(x^2)/2-x+1/6 e^{-3x}

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(d^2y)/(dx^2)+(dy)/(dx)=x+e^{-3x}

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

y = c_{1} + c_{2} e^{- x} + \frac{x ^{2}}{2} - x + \frac{1}{6} e^{- 3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{x ^{2}}{2} - x + \frac{1}{6} e^{- 3 x}

y = c_{1} + c_{2} e^{- x} + \frac{x ^{2}}{2} - x + \frac{1}{6} e^{- 3 x}

y^{^{''}} + 4 y - 5 = 0

y^{^{''}} - 8 y^{^{'}} - 20 y = 270 e^{x}

y^{^{''}} + 2 y^{^{'}} + y = ln (x) e^{- x}

y^{^{''}} + 10 y^{^{'}} + 25 y = x, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 6 y = 3 x e^{x}

What is the solution for (d^2y)/(dx^2)+(dy)/(dx)=x+e^{-3x} ?
The solution for (d^2y)/(dx^2)+(dy)/(dx)=x+e^{-3x} is y=c_{1}+c_{2}e^{-x}+(x^2)/2-x+1/6 e^{-3x}