What is the solution for (dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y) ?

The solution for (dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y) is y=-\W((6ln(x)+c_{1})/e)x-x

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(dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y)

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

y = - W (\frac{6 ln ( x ) + c _{1}}{e}) x - x

Solution steps

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

Solve using substitution:

y = - W (\frac{6 ln ( x ) + c _{1}}{e}) x - x

y = - W (\frac{6 ln ( x ) + c _{1}}{e}) x - x

x \to 0 + lim (- x)

\int sec (x) tan (x) - 6 e^{x} d x

y^{^{'}} = 5 (y - t^{2})

x y^{^{'}} + 2 y + x = 1

\frac{d}{d x} (x (x - 9)^{2})

What is the solution for (dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y) ?
The solution for (dy)/(dx)=(6x^4e^{y/x}+x^2y^2)/(x^3y) is y=-\W((6ln(x)+c_{1})/e)x-x