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

A curve, $C$ , passes through the point with coordinates $(3, 2)$ . The gradient of $C$ at any point $(x, y)$ is given by the differential equation

\frac{dy}{dx} = \frac{y^2(2x - 3)}{6}

Prove that $C$ intersects the coordinate axes at exactly one point and determine the coordinates of this point. Fully justify your answer.

[6]

A curve, $C$ , passes through the point with coordinates $(3, 2)$ . The gradient of $C$ at any point $(x, y)$ is given by the differential equation

\frac{dy}{dx} = \frac{y^2(2x - 3)}{6}

Prove that $C$ intersects the coordinate axes at exactly one point and determine the coordinates of this point. Fully justify your answer.

[6]

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