A) \[\frac{4}{5}\]
B) \[-\frac{2}{5}\]
C) \[-\frac{4}{5}\]
D) \[\frac{2}{5}\]
Correct Answer: A
Solution :
Given differential equation \[ydx+x{{y}^{2}}dx=xdy\] \[\Rightarrow \]\[\frac{xdy-ydx}{{{y}^{2}}}=xdx\]\[\Rightarrow \]\[-d\left( \frac{x}{y} \right)=d\left( \frac{{{x}^{2}}}{2} \right)\] Integrating we get\[-\frac{x}{y}=\frac{{{x}^{2}}}{2}+C\] \[\because \]It passes through (1, ?1) \[\therefore \]\[1=\frac{1}{2}+C\Rightarrow C=\frac{1}{2}\] \[\therefore \]\[{{x}^{2}}+1+\frac{2x}{y}=0\Rightarrow y=\frac{-2x}{{{x}^{2}}+1}\] \[\therefore \]\[f\left( -\frac{1}{2} \right)=\frac{4}{5}\]You need to login to perform this action.
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