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

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

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

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

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

sin (2 t) sin (t)

\int n x e^{n θ} e^{- x n} d x

\frac{\partial}{\partial x} (\frac{432}{y} + 3 y)

\frac{d}{d x} (x^{3} - 1)

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