Question

The slope field for a differential equation is shown in the figure. Determine the general solution of this equation.

100 POINTS
slope field with positive slopes in quadrant 1 and 4, negative slopes in quadrants 2 and 3, horizontal slopes along the y axis

y=Cx2
x=Cy2
x2 – y2 = C2
x2 + y2 = C2

Answer 1

`y=Cx^2`

Explanation:

Clearly,
`(dy)/(dx)` is a function of x, so we can eliminate the second option.

The slope field does not resemble a circle nor hyperbola, so we can eliminate the last two options.

This leaves us with
`y=Cx^2` as our general solution.