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

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

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

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

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

Solution steps

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

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}

\int 2 e^{x} d x

\int (3 x + 1)^{2} d x

sin^{2} (3 x)

t \to 1 lim (ln (t))

\frac{\partial}{\partial y} (x e^{y} + cos (y))

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