Question

Find the equation of the curve passing through (2, 2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point.

Answer 1

It is given that

dy/dx = 1/y

ydy = dx

Integrating, we get

y²/2 = x + c

which is passing through (2, 2), so, c = 0

Hence, the equation of the curve is

y² = 2x