Question: Suppose that the first-order differential equation dy/dx = f (x, y) possesses a one-parameter family of solutions and that f (x, y) satisfies the hypotheses

Suppose that the first-order differential equation dy/dx = f (x, y) possesses a one-parameter family of solutions and that f (x, y) satisfies the hypotheses of Theorem 1.2.1 in some rectangular region R of the xy-plane. Explain why two different solution curves cannot intersect or be tangent to each other at a point (x₀, y₀) in R.

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