Exercises

01

Hopping from a line

Consider the IVP: $y^{\prime }=1+2\sqrt{y-t},y(0)=0$. Show that the (differentiable) functional solutions can extend along the line $y(t)=t$ for arbitrary time in the forward direction, and at some moment deviate from the line following a certain parabola. Can the same happen in the reverse direction?

You are encouraged to understand the differential equation using the Desmos graph at https://www.desmos.com/calculator/sdxp7or83y.