slope fields
Introduction
Slope fields can be used to solve differential equations. Play with the app below and find the solution curves and its equation to the following functions:
1. f'(x, y) = x
2. f'(x, y) = y
3. f'(x, y) = x + y
4. f'(x, y) = 2x^2 - 3y
5. f'(x, y) = -x/y
6. f'(x, y) = ln(x)/y
Conjectures
What did you notice? When the derivative was equal to 1, what slope did it have? What about when the derivative was equal to 0? Negative? Relate these answers to the direction & magnitude of the lines.
Finding Solutions & Curves
In the leftmost box, type in "SolveODE( <function>, (x-value, y-value))" and see what equation you get. For ,function. type in the differential equation we are trying to solve and put in whatever x/y values you want to look at.