The order and degree of the differential equation of the family of curves $y=a(x+b)$ where a, b are arbitrary constants, are respectively.

2, 1

The correct answer is option (2) → 2, 1

$y=a(x+b)$

No. of independent arbitrary constants = 2

order will be = 2

$\frac{dy}{dx}=ax$  ...(1)

differentiating again wrt x

$\frac{d^2y}{dx^2}=a$ from (1)

$\frac{d^2y}{dx^2}=\frac{1}{x}\frac{dy}{dx}$

order → 2, degree → 1