Skip to content
dronacharya.ai
← JEE Main 2016 · 3 Apr · Shift 1
MathematicsSingle correct+4 / -1Question 77 of 90

JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 77

If a curve y = f(x) passes through the point (1, −1) and satisfies the differential equation, y(1+xy) dx=x dyy(1+xy)\,dx=x\,dy, then f(−12)f\left(-\dfrac12\right) is equal to :

Choose one option
Answer and worked solution

Official answer: D

y dx−x dy=−xy2dxy\,dx-x\,dy=-xy^2dx, so d(xy)=−x dxd\left(\frac xy\right)=-x\,dx and xy=−x22+c\frac xy=-\frac{x^2}2+c. Through (1, −1), c=−12c=-\frac12, so y=−2xx2+1y=-\dfrac{2x}{x^2+1} and f(−12)=15/4=45f\left(-\frac12\right)=\dfrac{1}{5/4}=\dfrac45.

Topics:Formation and applications
← Previous questionNext question →