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Exercise 105

Avg difficulty 3.5

Suppose f(y)={0 if y>0,1 if y≤0.f(y) = \begin{cases} 0 & \text{ if $y > 0$}, \\ 1 & \text{ if $y \leq 0$} . \end{cases} Does y′=f(y)y' = f(y), y(0)=0y(0) = 0 have a continuously differentiable solution? Does Picard apply? Why, or why not?

Lebl, Notes on Diffy Qs, §1.2 Slope fields, exercise 105

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.