Determining Existence and Uniqueness

[Ian Baughman]

Homework Statement

Determine whether existence of at least one solution of the given initial value problem is guaranteed and, if so, whether uniqueness of the solution is guaranteed.

dy/dx=y^(1/3); y(0)=0

Homework Equations

Existence and Uniqueness of Solutions Theorem:

Suppose that both the function ƒ(x,y) and its partial derivative [D][/y]f(x,y) are continuous on some rectangle R in the xy-plane that contains the point (a,b) in its interior. Then, for some open interval I containing the point a, the initial value problem

dy/dx=ƒ(x,y), y(a)=b

has one and only one solution that is defined on the interval I.

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

Determine whether existence of at least one solution of the given initial value problem is guaranteed and, if so, whether uniqueness of the solution is guaranteed.

dy/dx=y^(1/3); y(0)=0

Homework Equations

Existence and Uniqueness of Solutions Theorem:

Suppose that both the function ƒ(x,y) and its partial derivative [D][/y]f(x,y) are continuous on some rectangle R in the xy-plane that contains the point (a,b) in its interior. Then, for some open interval I containing the point a, the initial value problem

dy/dx=ƒ(x,y), y(a)=b

has one and only one solution that is defined on the interval I.

The Attempt at a Solution

So, what have you tried? You have to show some effort in this forum. Does the theorem apply to your problem? Have you looked for solution(s)? Show us what you are thinking...