The solution of the differential equation $y d x+\left(x+x^2 y\right) d y=0$ is

The solution of the differential equation $y d x+\left(x+x^2 y\right) d y=0$ is
  1. $-\frac{1}{x y}=C$
  2. $-\frac{1}{x y}+\log y=C$
  3. $\frac{1}{x y}+\log y=C$
  4. $\log y=C x$

Solution

$y d x+x d y+x^2 y d y=0$ $\frac{d(x y)}{x^2 y^2}+\frac{1}{y} d y=0 \Rightarrow-\frac{1}{x y}+\log y=C$

Asked in: JEE Main 2004

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