Question: Show that for a linear ODE y' + p(x)y = r(x) with continuous p and r in |x - x 0 | < a Lipschitz

Show that for a linear ODE y' + p(x)y = r(x) with continuous p and r in |x - x₀| < a Lipschitz condition holds. This is remarkable because it means that for a linear ODE the continuity of f(x, y) guarantees not only the existence but also the uniqueness of the solution of an initial value problem.

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