- #1
prosteve037
- 110
- 3
I'm having trouble understanding what uniqueness is/means. When given a slope/direction field I don't know what I should be looking for if asked to determine if a given initial condition has a unique solution.
Example:
[itex]\textit{y' = }\frac{(x - 1)}{y}[/itex]
With this equation I can see that as long as [itex]\textit{y ≠ 0}[/itex] a solution exists.
But now if I'm asked to find a given interval where a solution exists and is unique, I'm confused :P What should I be looking for in the equation/direction field?Here's the direction field for that differential equation:
Example:
[itex]\textit{y' = }\frac{(x - 1)}{y}[/itex]
With this equation I can see that as long as [itex]\textit{y ≠ 0}[/itex] a solution exists.
But now if I'm asked to find a given interval where a solution exists and is unique, I'm confused :P What should I be looking for in the equation/direction field?Here's the direction field for that differential equation: