| Exam Board | CAIE |
|---|
| Module | P3 (Pure Mathematics 3) |
|---|
| Year | 2018 |
|---|
| Session | November |
|---|
| Topic | First 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 \(x\).