CAIE P3 2023 November — Question 11

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicFirst order differential equations (integrating factor)

11 The variables \(x\) and \(y\) satisfy the differential equation $$x ^ { 2 } \frac { \mathrm {~d} y } { \mathrm {~d} x } + y ^ { 2 } + y = 0$$ It is given that \(x = 1\) when \(y = 1\).
  1. Solve the differential equation to obtain an expression for \(y\) in terms of \(x\).
  2. State what happens to the value of \(y\) when \(x\) tends to infinity. Give your answer in an exact form.
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