What is the solution for (dy)/(dx)=(y^2-x^2)/(xy) ?

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

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(dy)/(dx)=(y^2-x^2)/(xy)

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

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

Solution steps

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

Solve Bernoulli ODE:

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

y = x - 2 ln (x) + c_{1}, y = - x - 2 ln (x) + c_{1}

\int x^{3} ln (3 x) d x

\frac{d}{d x} (- 0.025 x^{2} + 8 x)

\int sin (ln (5 x)) d x

\frac{d}{d x} (\frac{x - 5}{x - 5})

\frac{\partial}{\partial x} (x^{2} y + \frac{1}{y})

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