What is the solution for (2xe^x-y+6x^2)dx-xdy=0 ?

The solution for (2xe^x-y+6x^2)dx-xdy=0 is y=2x^2+(2(e^xx-e^x))/x+(c_{1})/x

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(2xe^x-y+6x^2)dx-xdy=0

(2 x e^{x} - y + 6 x^{2}) d x - x d y = 0

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

Solution steps

(2 x e^{x} - y + 6 x^{2}) d x - x d y = 0

Solve linear ODE:

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

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

(7, - 1), (0, - 6)

\int \frac{1}{x - 2} d x

\int \frac{5}{u u ^{2} - 1} d u

f (t) = \frac{9}{t}

\frac{d}{d x} (\frac{x - 5}{x ^{2} + 1})

What is the solution for (2xe^x-y+6x^2)dx-xdy=0 ?
The solution for (2xe^x-y+6x^2)dx-xdy=0 is y=2x^2+(2(e^xx-e^x))/x+(c_{1})/x