| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2022 |
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| Session | June |
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| Topic | First order differential equations (integrating factor) |
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4 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x y } { 1 + x ^ { 2 } }$$
and \(y = 2\) when \(x = 0\).
Solve the differential equation, obtaining a simplified expression for \(y\) in terms of \(x\).