What is the solution for y^'=(6x^2+y^2)/(xy) ?

The solution for y^'=(6x^2+y^2)/(xy) is y=xsqrt(12ln(x)+c_{1)},y=-xsqrt(12ln(x)+c_{1)}

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y^'=(6x^2+y^2)/(xy)

y^{^{'}} = \frac{6 x ^{2} + y ^{2}}{x y}

y = x 12 ln (x) + c_{1}, y = - x 12 ln (x) + c_{1}

Solution steps

y^{'} (x) = \frac{6 x ^{2} + y ^{2}}{x y}

Solve Bernoulli ODE:

y = x 12 ln (x) + c_{1}, y = - x 12 ln (x) + c_{1}

y = x 12 ln (x) + c_{1}, y = - x 12 ln (x) + c_{1}

\int y e^{x y} d x

\int x 5 x + 1 d x

y^{^{'}} = \frac{( e ^{x - y} )}{1 + e ^{x}}, y (1) = 0

x \to 2 + lim (2 x - [∣ x ∣])

x \to 0 lim (\frac{( x ^{2} + x )}{x})

What is the solution for y^'=(6x^2+y^2)/(xy) ?
The solution for y^'=(6x^2+y^2)/(xy) is y=xsqrt(12ln(x)+c_{1)},y=-xsqrt(12ln(x)+c_{1)}