| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2014 |
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| Session | June |
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| Topic | First order differential equations (integrating factor) |
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5 The variables \(x\) and \(\theta\) satisfy the differential equation
$$2 \cos ^ { 2 } \theta \frac { \mathrm {~d} x } { \mathrm {~d} \theta } = \sqrt { } ( 2 x + 1 )$$
and \(x = 0\) when \(\theta = \frac { 1 } { 4 } \pi\). Solve the differential equation and obtain an expression for \(x\) in terms of \(\theta\).