Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The diagram shows the tangent to the curve at $P$, where $P$ has coordinates $(x, y)$, and this tangent cuts the $x$-axis at $T$. $N$ is the point where the perpendicular from $P$ meets the $x$-axis. For every $x$, the curve has a positive gradient, and $TN = 2$.
(i)[1]
Show that the differential equation linking $x$ and $y$ is $\frac{dy}{dx} = \frac{1}{2}y$.
(ii)[5]
The curve passes through the point $(4, 3)$. Solve the differential equation to find the equation of the curve, with $y$ written as a function of $x$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give a complete justification by using gradient of curve equals gradient of the tangent” …