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

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

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

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

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}} d x

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

f (x) = 7 cos (x), at (\frac{2 π}{3})

x \to 1 lim (\frac{2 - x}{x - 1})

\frac{d}{d x} (x \cdot 2)

(10.1) (5.2)

\int \frac{1}{x ^{2} - x} d x

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