Question

A slope field has curves going through (0, 0), a minimum at (0.5, -0.5), and a maximum at (1.5, 0.5). Which equation could represent a particular solution to the differential equation?

A) y=x^2
B) y=−x^2
C) y=e^x
D) y=−e^x

Answer 1

The equation that could represent a particular solution to the differential equation is y=e^x (Option C).

Step-by-step explanation:

The equation that could represent a particular solution to the differential equation is y=e^x (Option C).

From the given information, we can determine that the curve begins at zero with an upward slope that increases in magnitude until it becomes a positive constant. This behavior matches the graph of the exponential function y=e^x.

Therefore, the equation y=e^x could represent a particular solution to the differential equation.