| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2023 |
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| Session | March |
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| Topic | First order differential equations (integrating factor) |
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9 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { e } ^ { 3 y } \sin ^ { 2 } 2 x$$
It is given that \(y = 0\) when \(x = 0\).
Solve the differential equation and find the value of \(y\) when \(x = \frac { 1 } { 2 }\).