Edexcel AEA 2008 June — Question 2

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2008
SessionJune
TopicFirst order differential equations (integrating factor)

2.The points \(( x , y )\) on the curve \(C\) satisfy $$( x + 1 ) ( x + 2 ) \frac { d y } { d x } = x y$$ The line with equation \(y = 2 x + 5\) is the tangent to \(C\) at a point \(P\) .
(a)Find the coordinates of \(P\) .
(b)Find the equation of \(C\) ,giving your answer in the form \(y = \mathrm { f } ( x )\) .