| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2021 |
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| Session | June |
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| Topic | First order differential equations (integrating factor) |
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7 A curve is such that the gradient at a general point with coordinates \(( x , y )\) is proportional to \(\frac { y } { \sqrt { x + 1 } }\). The curve passes through the points with coordinates \(( 0,1 )\) and \(( 3 , e )\).
By setting up and solving a differential equation, find the equation of the curve, expressing \(y\) in terms of \(x\).