What is the solution for 2xy^'=2xe^x-2y+6x^2 ?

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

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2xy^'=2xe^x-2y+6x^2

2 x y^{^{'}} = 2 x e^{x} - 2 y + 6 x^{2}

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

Solution steps

2 x y^{'} (x) = 2 x e^{x} - 2 y + 6 x^{2}

Solve linear ODE:

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

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

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