CAIE P3 2018 November — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionNovember
TopicFirst order differential equations (integrating factor)

5 The coordinates \(( x , y )\) of a general point on a curve satisfy the differential equation $$x \frac { \mathrm {~d} y } { \mathrm {~d} x } = \left( 2 - x ^ { 2 } \right) y .$$ The curve passes through the point \(( 1,1 )\). Find the equation of the curve, obtaining an expression for \(y\) in terms of \(x\).
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