What is the solution for (dy)/(dx)=(xy)/(ln(y)) ?

The solution for (dy)/(dx)=(xy)/(ln(y)) is y=e^{sqrt(x^2+c_{1)}},y=e^{-sqrt(x^2+c_{1)}}

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(dy)/(dx)=(xy)/(ln(y))

\frac{d y}{d x} = \frac{x y}{ln ( y )}

y = e^{x^{2} + c_{1}}, y = e^{- x^{2} + c_{1}}

Solution steps

\frac{d y}{d x} = \frac{x y}{ln ( y )}

Solve separable ODE:

y = e^{x^{2} + c_{1}}, y = e^{- x^{2} + c_{1}}

y = e^{x^{2} + c_{1}}, y = e^{- x^{2} + c_{1}}

(1 - x) y^{^{'}} - y^{2} = 0

y^{^{'}} = 2 y - 3

\frac{d y}{d x} = \frac{y + 2 x y}{x ^{2}}

(1 - y) e^{y} y^{^{'}} + \frac{y ^{2}}{x ln ( x )} = 0

2 x \frac{d y}{d x} = cos^{2} (y), y (0) = 2

What is the solution for (dy)/(dx)=(xy)/(ln(y)) ?
The solution for (dy)/(dx)=(xy)/(ln(y)) is y=e^{sqrt(x^2+c_{1)}},y=e^{-sqrt(x^2+c_{1)}}