Form the differentilal equation of all lines which makes intercep… - Vidyadip

Question

Form the differentilal equation of all lines which makes intercept 3 on $x$-axis.

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Answer

All lines having $x$ - intercept 3 pass through the point $(3,0)$
Let $m$ be the slope of the line
$\therefore$ Its equation is
$
\begin{aligned}
\therefore y-0 & =m(x-3) ...(1) \\
\text { 1.e. } y & =m x-3 m \\
\therefore \frac{d y}{d x} & =m
\end{aligned}
$
Substituting this value of $m$ in (1)
$
y=\frac{d y}{d x}(x-3)
$
or $y d x=(x-3) d y$ is the required differential equation.

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