The equation of the family of curves shown in the figure with one arbitrary constant.
Step-by-Step Solution
Key Concept: A family of curves with one arbitrary constant yields a first-order differential equation
From the figure, the family of curves appears to be straight lines passing through the origin with varying slopes. The equation representing such a family with one arbitrary constant is $y = kx$, where $k$ is the arbitrary constant. The order of the differential equation will be 1.
Correct Answer: 1