What is the solution for yln(y)dx+(x-ln(y))dy=0 ?

The solution for yln(y)dx+(x-ln(y))dy=0 is y=e^{x-sqrt(x^2-c_{1)}},y=e^{x+sqrt(x^2-c_{1)}}

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yln(y)dx+(x-ln(y))dy=0

y ln (y) d x + (x - ln (y)) d y = 0

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

Solution steps

y ln (y) d x + (x - ln (y)) d y = 0

Solve exact ODE:

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

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

\frac{\partial}{\partial x} (x^{3} y + e^{x y^{2}})

\frac{d y}{d x} = 1 - 2 y

\int tan^{5} (8 x) sec^{4} (8 x) d x

f (x) = \frac{1}{3 x}

(4 x)^{10 x^{3}}

What is the solution for yln(y)dx+(x-ln(y))dy=0 ?
The solution for yln(y)dx+(x-ln(y))dy=0 is y=e^{x-sqrt(x^2-c_{1)}},y=e^{x+sqrt(x^2-c_{1)}}