A) \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+c\]
B) \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+c\]
C) \[\log \left( xy \right)=\frac{1}{x}+\frac{1}{y}+c\]
D) \[\log \left( xy \right)+\frac{1}{x}+\frac{1}{y}=c\]
Correct Answer: A
Solution :
The given equation \[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\]Þ\[\frac{1-y}{{{y}^{2}}}dy+\frac{1+x}{{{x}^{2}}}dx=0\] Þ \[\left( \frac{1}{{{y}^{2}}}-\frac{1}{y} \right)dy+\left( \frac{1}{{{x}^{2}}}+\frac{1}{x} \right)dx=0\] On integrating, we get the required solution \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+c\].You need to login to perform this action.
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