(a(i))[9]
Solve the differential equation, find the value of $k$, and write $x$ in terms of $t$.
(a(ii))[1]
State what value $x$ approaches when $t$ becomes large.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $t$ are connected by the differential equation $t \frac{dx}{dt} = \frac{k - x^3}{2x^2}$, for $t > 0$, where $k$ is a constant. When $t = 1$, $x = 1$ and when $t = 4$, $x = 2$.