A) \[x{{y}^{2}}=c\]
B) \[{{x}^{2}}{{y}^{2}}=c\]
C) \[{{x}^{2}}y=c\]
D) \[xy=c\]
Correct Answer: C
Solution :
\[{{x}^{2}}dy=-2xydx\] Þ \[\frac{1}{y}dy=-\frac{2x}{{{x}^{2}}}dx\] On integrating, \[\log y=-2\log x+\log c\] Þ \[\log y=\log {{x}^{-2}}+\log c\]Þ \[\log y{{x}^{2}}=\log c\]or \[y{{x}^{2}}=c\].
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