| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2016 |
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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
$$x \frac { \mathrm {~d} y } { \mathrm {~d} x } = y \left( 1 - 2 x ^ { 2 } \right)$$
and it is given that \(y = 2\) when \(x = 1\). Solve the differential equation and obtain an expression for \(y\) in terms of \(x\) in a form not involving logarithms.