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$If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation y(1+xy)dx=xdy then$ $f (- \frac{1}{2}) is$

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Correct option is C

ydx+xy2dx=xdyydx-xdy=-xy2dx∫ydx−xdyy2=−∫xdx→∫d(x/y)=−x22+c→xy+x22=c which passes through (1,-1)→c=−12⇒xy+x22=−12⇒ put x=−12⇒−12y+1/42=−12⇒−12y=−18−12=−58−12y=−58⇒y=45

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If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation y(1+xy)dx=xdy then f −12 is

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Ready to Test Your Skills?

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$If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation y(1+xy)dx=xdy then$ $f (- \frac{1}{2}) is$