CAIE A-Level Mathematics A2 3.8.4 Differential Equations Questions

Practise interpreting differential-equation models, long-term behaviour and parameter effects.

Exam points

interpret solutions and long-term behaviour of differential-equation models
use derivatives and limits to analyse model predictions
relate model parameters and initial conditions to context

[Maximum number: 1]

The variables x and y satisfy the differential equation

x^{2} \frac{\mathrm{~d} y}{\mathrm{~d} x}+y^{2}+y=0 .

It is given that x=1 when y=1.

State what happens to the value of y when x tends to infinity. Give your answer in an exact form.

State that y approaches $\frac{1}{2 \mathrm{e}-1}$

B1 FT

Or exact equivalent. Condone $y=\frac{1}{2 \mathrm{e}-1}$ .
FT on an expression in $\mathrm{e}^{\frac{1}{x}}$ .

B1ft

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CAIE A-Level Mathematics A2 3.8.4 Differential Equations Questions question 1