Solving a problem regarding Existence theorem.

[bravoman]

Homework Statement

Given the equation dy/dx = y^4 - x^4, y(0) = 7, determine whether the existence/uniqueness theorem implies that the given initial value problem has a unique solution.

Homework Equations

Existence/Uniqueness Theorem

The Attempt at a Solution

To my understanding, you must assign f(x,y) = y^4 - x^4 then derive f(x,y) in terms of y.

f'(x,y) = 4y^3

This is as far as I have gotten.

 

[Ray Vickson]

Homework Statement

Given the equation dy/dx = y^4 - x^4, y(0) = 7, determine whether the existence/uniqueness theorem implies that the given initial value problem has a unique solution.

Homework Equations

Existence/Uniqueness Theorem

The Attempt at a Solution

To my understanding, you must assign f(x,y) = y^4 - x^4 then derive f(x,y) in terms of y.

f'(x,y) = 4y^3

This is as far as I have gotten.

What is the statement of the existence/uniqueness theorem? How does it apply in your case?

 

[bravoman]

I need to use the theorem to determine of the equation dy/dx = y^4 - x^4 has a unique solution at point (0,7). Is that correct?

 

[Mark44]

What is the statement of the existence/uniqueness theorem? How does it apply in your case?

I need to use the theorem to determine of the equation dy/dx = y^4 - x^4 has a unique solution at point (0,7). Is that correct?

That isn't what Ray asked. What does the Existence and Uniqueness Theorem say?