Question

The solution of $\left(y\right(1+x^{-1})+siny)dx+(x+logx+xcosy)dy=0$ is

• A. $(1+y^{-1}siny)+x^{-1}logx=C$
  
• B. $(y+siny)+xylogx=C$
  
• C. $xy+ylogx+xsiny=C$
• D. $Noneofthese$

Answer 1

The correct option is C $xy+ylogx+xsiny=C$

The given equation can be written as $y(1+x^{-1})dx+(x+logx)dy+sinydx+xcosydy=0$
$\Rightarrow d\left(y\right(x+logx\left)\right)+d\left(xsiny\right)=0\to y(x+logx)+xsiny=C$