The general solution of $\left( x - y \cos \left( \frac { y } { x } \right) \right) d x + x \cos \left( \frac { y } { x } \right) d y = 0$ is

A) $\ln x - \sin \left( \frac { y } { x } \right) = c$
B) $\ln x + \sin \left( \frac { y } { x } \right) = c$
C) $\ln x - \sin \left( \frac { x } { y } \right) = c$
D) $\ln x + \sin \left( \frac { x } { y } \right) = c$
E) $\ln y - \sin \left( \frac { x } { y } \right) = c$

Question

The general solution of $\left( x - y \cos \left( \frac { y } { x } \right) \right) d x + x \cos \left( \frac { y } { x } \right) d y = 0$ is

A) $\ln x - \sin \left( \frac { y } { x } \right) = c$
B) $\ln x + \sin \left( \frac { y } { x } \right) = c$
C) $\ln x - \sin \left( \frac { x } { y } \right) = c$
D) $\ln x + \sin \left( \frac { x } { y } \right) = c$
E) $\ln y - \sin \left( \frac { x } { y } \right) = c$

Quizplus · Accepted Answer

The given differential equation can be rewritten as $\frac{dx}{x} = \frac{\cos(y/x)dy}{\cos(y/x)}$, integrating both sides gives $\ln x + \sin(y/x) = c$, which matches choice B.

The General Solution Of (x−ycos⁡(yx))dx+xcos⁡(yx)dy=0\left( x - y \cos \left( \frac { y } { x } \right) \right) d x + x \cos \left( \frac { y } { x } \right) d y = 0(x−ycos(xy​))dx+xcos(xy​)dy=0

The General Solution Of $\left( x - y \cos \left( \frac { y } { x } \right) \right) d x + x \cos \left( \frac { y } { x } \right) d y = 0$