Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The variables $x$ and $t$ are linked by the differential equation $5\frac{dx}{dt} = (20 - x)(40 - x)$. You are told that $x = 10$ when $t = 0$.
(a(i))[9]
With partial fractions, solve the differential equation and produce an expression for $x$ in terms of $t$.
(i)[9]
With partial fractions, solve the differential equation and produce an expression for $x$ in terms of $t$.
(ii)[1]
State how the value of $x$ changes when $t$ is very large.
Worked solution & mark scheme
This 19-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Separate the variables correctly and carry out one integration.” …