The solution of $( x - 2 y ) d x + y d y = 0$ is
A) $\ln ( y - x ) - x / ( y - x ) = c$
B) $\ln ( y - x ) - x / ( y - x ) + c$
C) $\ln x + \ln ( y - x ) = c$
D) $\ln ( ( y - x ) / x ) = c$
E) it cannot be solved

Question

Quizplus · Accepted Answer

The equation is exact because $ \frac{\partial}{\partial y} (x - 2y) = \frac{\partial}{\partial x} y $. The solution is found by integrating $ x - 2y $ with respect to $ x $ and $ y $ with respect to $ y $, respectively, and then combining the results.

The Solution Of (x−2y)dx+ydy=0( x - 2 y ) d x + y d y = 0(x−2y)dx+ydy=0

The Solution Of $( x - 2 y ) d x + y d y = 0$