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

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

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

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

\int \frac{1}{3 - 8 x} d x

- \frac{x}{( 25 - x ^{2} ) ^{\frac{1}{2}}}

(125 + x)^{- \frac{1}{3}}

y^{^{''}} + 2 y^{^{'}} + y = 14 e^{- t}

\int cos^{3} (3 x) d x

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