Slope fields

Reading the shape and long-run behavior of solution curves off a field of short tangent segments, plus when existence and uniqueness are guaranteed.

Notes on Diffy Qs: Differential Equations for Engineers, Slope fields

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4 exercises

Exercise 102

Is it possible to solve $y' = xy$ for $y(0) = 0$ ? Is the solution unique?

2.5

Exercise 103

Is it possible to solve $y' = \frac{x}{x^2-1}$ for $y(1) = 0$ ?

2.5

Exercise 105

Suppose Does $y' = f(y)$ , $y(0) = 0$ have a continuously differentiable solution? Does Picard apply? Why, or why not?

3.5

Exercise 106

Consider an equation of the form $y' = f(x)$ for some continuous function $f$ , and an initial condition $y(x_0) = y_0$ . Does a solution exist for all $x$ ? Why or why not?

2.5