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Solution of differential equation $x dy-y dx=0$ represents:

\[(A)\;a\; rectangular\; hyperbola\quad(B)\;parabola\; whose\; vertex \;is\; at \;origin \quad(C)\;straight \;line\; passing\; through \;origin \quad(D)\;a \;circle\; whose\; centre\; is\; at\; origin \]

1 Answer

  • If an equation has n arbitary constants. then its differential equation will be of $n^{th}$ order
  • Equation of a straight line pasing through the orgin is $y=mx$
Let us consider the equation of a stright line $y=mx$, which passes through the orgin.
Now differentiation with respect to x we get,
Substituting this for m in $y=mx$ we get
or $xdy-ydx=0$
Hence the correct option is $C$
answered May 21, 2013 by meena.p

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