(adsbygoogle = window.adsbygoogle || []).push({}); Need help with ODE and "Existence and Uniqueness Thm"

I'm currently helping my neice study for her exams and going though last years test there was this one question that I wasn't sure about.

-------------

Considering the initial value problem,

[tex]\frac{dy}{dx} = f(x,y)[/tex]

Where [tex]f(x,y) = (1+x) \sqrt{y}[/tex] and y(1)=0.

Does the "Existence and Uniqueness Theorem" guarantee the existence of a unique solution?

-------------

I'm pretty sure that the theorem they are referring to is this one,

http://mathworld.wolfram.com/PicardsExistenceTheorem.html

See also,

http://www.utpb.edu/scimath/wkfield/mod3/Exuni.htm [Broken]

I'm thinking that it (the Theorem) doesn't guarantee a unique solution because [tex]\frac{\partial f}{\partial y}[/tex] is not well defined at the initial condition y=0.

Unfortunately I'm not too familiar with this "Existence and Uniqueness" theorem. Also the DE does seem to have a well defined solution of y(x)=0 for x>=1, so I'm really not sure. Can anyone help me out here, thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need help with ODE and Existence and Uniqueness Thm

**Physics Forums | Science Articles, Homework Help, Discussion**