Let D=(x,y)inmathbb R^2:-1le xle1, -1le yle1, and f:Dtomathbb R be the function defined by f(x,y)=1+sqrty+,quadwhere y+=maxy,0. Consider the initial value problem (IVP) dy/dx=f(x,y),quad y(0)=0. Then which of the following statements are true?

Q91Section C (Part C)91 of 120

Non-Lipschitz right-hand side $1+\sqrt{y_+}$ and Peano existence

Let $D=\{(x,y)\in\mathbb R^2:-1\le x\le1, -1\le y\le1\}$ , and $f:D\to\mathbb R$ be the function defined by

$f(x,y)=1+\sqrt{y_+},\quad\text{where }y_+=\max\{y,0\}.$

Consider the initial value problem (IVP)

$\frac{dy}{dx}=f(x,y),\quad y(0)=0.$

Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

Keyboard: A–D answer · S solution · ←/→ previous/next