What is the solution for (dy)/(dx)+6xy=2x ?

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

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(dy)/(dx)+6xy=2x

\frac{d y}{d x} + 6 x y = 2 x

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

Solution steps

\frac{d y}{d x} + 6 x y = 2 x

Solve separable ODE:

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

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

4 y y^{^{'}} = x + x y^{2}

y^{^{'}} = x y^{\frac{1}{2}}

x y d y + y d x + 4 y d y + 3 d x = 8 d y + 3 x d x + 2 x d y + x y d x

f (x) = \frac{df}{d x}

\frac{d y}{d x} = \frac{x ^{3}}{2 y}

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