| 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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8 The variables \(x\) and \(y\) satisfy the differential equation
$$\mathrm { e } ^ { 4 x } \frac { \mathrm {~d} y } { \mathrm {~d} x } = \cos ^ { 2 } 3 y .$$
It is given that \(y = 0\) when \(x = 2\).
Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).