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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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