| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2022 |
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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
$$( x + 1 ) ( 3 x + 1 ) \frac { \mathrm { d } y } { \mathrm {~d} x } = y$$
and it is given that \(y = 1\) when \(x = 1\).
Solve the differential equation and find the exact value of \(y\) when \(x = 3\), giving your answer in a simplified form.