What is the solution for xdy-ydx=(xy)^{1/2} ?

The solution for xdy-ydx=(xy)^{1/2} is y= 1/4 xln^2(x)+c_{1}xln(x)+c_{1}^2x

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xdy-ydx=(xy)^{1/2}

x d y - y d x = (x y)^{\frac{1}{2}}

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x

Solution steps

x d y - y d x = (x y)^{\frac{1}{2}}

Solve Bernoulli ODE:

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x

\frac{\partial}{\partial x} (6 e^{x^{5} y})

\int_{0}^{1} \frac{x - 1}{x} d x

g (x) = - 3 x^{2} + 5 x - 6

6 x

\int \frac{( x - 1 )}{2} d x

What is the solution for xdy-ydx=(xy)^{1/2} ?
The solution for xdy-ydx=(xy)^{1/2} is y= 1/4 xln^2(x)+c_{1}xln(x)+c_{1}^2x