Question

Form a differential equation representing the given family
of curves by eliminating arbitrary constant a and b.

$\frac{x}{a}+\frac{y}{b}=1$

Answer 1

The number of times we differentiate is equal to the number of constants in the equation.

$\frac{x}{a}+\frac{y}{b}=1$

Differentiating,we get,

$\frac{1}{a}+\frac{1}{b}\frac{dy}{dx}=0$

$\frac{dy}{dx}=-\frac{b}{a}$

Differentiating again, we get

$\frac{d^{2}y}{d{x}^2}=0$

$y^{{}^{\prime \prime }}=0$ is the required differential equation