The profile of a cooling fin in a high-performance engine is modeled by a curve CCC in the (x,y)(x, y)(x,y) plane. For y>0y > 0y>0, the gradient of the curve at any point (x,y)(x, y)(x,y) is given by the differential equation
dydx=x3y227 \frac{dy}{dx} = \frac{x^3 y^2}{27} dxdy=27x3y2The curve CCC passes through the point with coordinates (3,1)(3, 1)(3,1). Show that CCC intersects the coordinate axes at exactly one point and state the coordinates of this point. Fully justify your answer.
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.