| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2020 |
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| Session | November |
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| Topic | First order differential equations (integrating factor) |
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8 The coordinates \(( x , y )\) of a general point of a curve satisfy the differential equation
$$x \frac { \mathrm {~d} y } { \mathrm {~d} x } = \left( 1 - 2 x ^ { 2 } \right) y$$
for \(x > 0\). It is given that \(y = 1\) when \(x = 1\).
Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).