Question

The slope of the tangent to a curve at any point is reciprocal of twice the ordinate of that point. The curve passes through (4,3). Formulate the differential equation and hence find the equation of the curve.

Answer 1

Let P(x,y) be any point on the curve.

Slope of tangent at P(x,y) = $\frac{dy}{dx}$

Therefore, according to question,

$\frac{dy}{dx}=\frac{1}{2y}$

$2ydy=dx$

Integrating both sides,

$y^2=x+C$

Since, the curve passes through (4,3), then,

$9=4+C$

$C=5$

Hence, the required equation of the curve is $y^2=x+5$.