What is the solution for (y+sqrt(xy))dx=xdy ?

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

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(y+sqrt(xy))dx=xdy

(y + x y) d x = x d y

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

Solution steps

(y + x y) d x = x d y

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

12 x^{2} + 3 x

f (x) = 4 - 5 x^{2}

x \to a lim (x - a + c)

n = 1 \sum \infty \frac{1}{5 ^{n}}

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