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}

y^{^{'}} = - x y, y (0) = 1

x (x - 1) \frac{d y}{d x} = y

\frac{d y}{d x} = (\frac{y}{20000}) x

(sin (x) sin (y)) d y = (cosh (x) cos (y)) d x

\frac{d x}{d t} = 60 - \frac{1}{100} x

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