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

        \frac{x}{a} + \frac{y}{b} = 1

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Given equation is

\frac{x}{a} + \frac{y}{b} = 1
Differentiate both the sides w.r.t x
\frac{d\left ( \frac{x}{a}+\frac{y}{b} \right )}{dx}=\frac{d(1)}{dx}
\frac{1}{a}+\frac{1}{b}.\frac{dy}{dx} = 0\\ \frac{dy}{dx} = -\frac{b}{a}
Now, again differentiate it w.r.t x
\frac{d^2y}{dx^2} =0
Therefore, the required differential equation is  \frac{d^2y}{dx^2} =0   or  y^{''} =0

Posted by

Gautam harsolia

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