A) \[2x+{{x}^{2}}y=\lambda y\]
B) \[2y+{{y}^{2}}x=\lambda y\]
C) \[2y-{{y}^{2}}x=\lambda y\]
D) None of these
Correct Answer: A
Solution :
\[\frac{ydx-xdy}{{{y}^{2}}}=-xdx\] Þ \[d\left( \frac{x}{y} \right)=-xdx\] Integrating both side, we get \[\frac{x}{y}=-\frac{{{x}^{2}}}{2}+c\] Þ \[2x+{{x}^{2}}y=2cy\] Þ \[2x+{{x}^{2}}y=\lambda y\] [\[\lambda =2c\]]
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