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.

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