Question

How do you sketch a slope field for `dy/dx = (x + 1)^2/y`?

Answer 1

The slope field is pretty much a bunch of lines that represent the slopes of the solution points. For instance, if we have the point `(0, 2)` is a solution to the differential equation above, you should find that the slope on the field should be `(0 + 1)^2/2 = 1/2`,

Here is the slope field for the given differential equation. The black curve would be one particular solution to the equation. A solution is given by following the slopes.

Hopefully this helps!