Existence and Uniqueness Theorem Checker: Step-by-Step Solutions

Test the hypotheses of the existence and uniqueness theorem at a point. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

The theorem: if $f$ and $\partial f/\partial y$ are continuous on a rectangle containing $(x_0,y_0)$ in its interior, the IVP has exactly one solution on some interval around $x_0$. Enter $f$ and the point.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 1.3: Initial-Value Problems, Boundary-Value Problems, and Existence of Solutions, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 1 quiz.

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