A curve, CCC, passes through the point with coordinates (3,2)(3, 2)(3,2). The gradient of CCC at any point (x,y)(x, y)(x,y) is given by the differential equation
dydx=y2(2x−3)6 \frac{dy}{dx} = \frac{y^2(2x - 3)}{6} dxdy=6y2(2x−3)Prove that CCC intersects the coordinate axes at exactly one point and determine the coordinates of this point. Fully justify your answer.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
