| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2023 |
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| Session | November |
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| Topic | First order differential equations (integrating factor) |
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7 The variables \(x\) and \(\theta\) satisfy the differential equation
$$\frac { x } { \tan \theta } \frac { \mathrm {~d} x } { \mathrm {~d} \theta } = x ^ { 2 } + 3$$
It is given that \(x = 1\) when \(\theta = 0\).
Solve the differential equation, obtaining an expression for \(x ^ { 2 }\) in terms of \(\theta\).