Question

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b:$\frac xa + \frac yb =1$

Answer 1

To form a differential equation,differentiate the given function and eliminate constants a and b

$\frac{x}{a} + \frac{y}{b} = 1 \: \: \: \: eq1 \\ \\ differentiate \: eq1 \\ \\ \frac{1}{a} + \frac{1}{b} \frac{dy}{dx} \: =0 \: \: \: \: eq2$
Differentiate eq2

$\frac{1}{b} \frac{ {d}^{2}y }{d {x}^{2} } = 0 \: \: \: eq3 \\ \\ \frac{ {d}^{2}y }{d {x}^{2} } = 0$

is the required differential equation.

Hope it helps you.