What is the solution for (6xdy)/(dx)=2xe^x-6y+6x^2 ?

The solution for (6xdy)/(dx)=2xe^x-6y+6x^2 is y=(e^xx-e^x}{3x}+\frac{x^2)/3+(c_{1})/x

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(6xdy)/(dx)=2xe^x-6y+6x^2

\frac{6 x d y}{d x} = 2 x e^{x} - 6 y + 6 x^{2}

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

Solution steps

\frac{6 x d y}{d x} = 2 x e^{x} - 6 y + 6 x^{2}

Solve linear ODE:

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

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

\frac{d}{d x} (30 ln (5 x + 1))

{\frac{4}{s} + \frac{6}{s ^{5}} - \frac{1}{s + 8}}

\int e^{2 z} d z

\frac{d}{d x} (arctan (x t))

\frac{\partial}{\partial x} (\frac{3 x}{x ^{2} + 2})

What is the solution for (6xdy)/(dx)=2xe^x-6y+6x^2 ?
The solution for (6xdy)/(dx)=2xe^x-6y+6x^2 is y=(e^xx-e^x}{3x}+\frac{x^2)/3+(c_{1})/x