alleryThe differential equation of the family of straight lines $y = mx + c$ (with $m, c$ arbitrary) is:
A$d^2y/dx^2 = 0$
B$dy/dx = 0$
C$d^2y/dx^2 = m$
D$y = x\,dy/dx$
Answer & Solution
Correct answer: A. $d^2y/dx^2 = 0$
Two arbitrary constants $m, c$ ⇒ second-order DE.
**Differentiate twice:** $dy/dx = m$, then $d^2y/dx^2 = 0$.
Every straight line has zero curvature.
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