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

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

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

6 x (\frac{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

6 x (\frac{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}

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