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1.11.7 Differential equations with separable variables (A-level only)

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Question 21

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.

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1.11.7 Differential equations with separable variables (A-level only) Questions

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