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Question 531

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.

[6]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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