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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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