A) a family of hyperbolas
B) a family of circles whose centres are on the y-axis
C) a family of parabolas
D) a family of circles whose centres are on the x-axis
Correct Answer: D
Solution :
Given differential equation is \[y\,\frac{dy}{dx}+x=c\] \[\Rightarrow \] \[y\,dy\,=\,(c-x)dx\] On integrating both sides, we get \[\frac{{{y}^{2}}}{2}=cx-\frac{{{x}^{2}}}{2}+d\] \[\Rightarrow \] \[{{y}^{2}}+{{x}^{2}}-2cx-2d=0\] Hence, it represents a family of circles whose centres are on the x-axis.
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