(a)[1]
State a differential equation linking $x$ and $y$.
(b)[5]
Solve the differential equation to find the equation of the curve, with $y$ written as a function of $x$.
(c)[1]
Sketch the curve clearly.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The diagram shows a moving point $P$ at $(x, y)$ and the point $N$, which is the foot of the perpendicular from $P$ to the $x$-axis. $P$ lies on a curve for which, whenever $x > 0$, the gradient of the curve is equal to the area of triangle $OPN$, where $O$ is the origin. The point $(0, 2)$ is on the curve.