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

The solution for dy-(y/x+x/y)dx=0 is y=xsqrt(2ln(x)+c_{1)},y=-xsqrt(2ln(x)+c_{1)}

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dy-(y/x+x/y)dx=0

d y - (\frac{y}{x} + \frac{x}{y}) d x = 0

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

Solution steps

d y - (\frac{y}{x} + \frac{x}{y}) d x = 0

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}

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