| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2023 |
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| Session | June |
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| Topic | First order differential equations (integrating factor) |
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8 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } + 4 } { x ( y + 4 ) }$$
for \(x > 0\). It is given that \(x = 4\) when \(y = 2 \sqrt { 3 }\).
Solve the differential equation to obtain the value of \(x\) when \(y = 2\).