UPSC NDA Math Model Paper 3

Given: the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates

dy

dx

=xy

1

y

dy=xdx Integrate, log‌y=

x2

2

+C ......(1)
Equation(1)passing through(1, 1)log(1)=

12

2

+C⇒C=−

1

2

Put in eq. (1)
⇒log‌y=

x2

2

−

1

2

⇒2‌log‌y=x2−1
Hence, option (3) is correct.