The differential equation of all family of lines $y=m x+\frac{4}{m}$ obtained by eliminating the arbitrary…
The differential equation of all family of lines $y=m x+\frac{4}{m}$ obtained by eliminating the arbitrary constant $\mathrm{m}$ is
- $y\left(\frac{d y}{d x}\right)=4$
- $y\left(\frac{d y}{d x}\right)^2+y\left(\frac{d y}{d x}\right)+4=0$
- $x\left(\frac{d y}{d x}\right)+4=0$
- $x\left(\frac{d y}{d x}\right)^2-y\left(\frac{d y}{d x}\right)+4=0$
Solution
$\begin{aligned}
& y=m x+\frac{4}{m} \\
& \therefore \frac{d y}{d x}=m
\end{aligned}$
Substituting value of $\mathrm{m}$ in equation (1), we get
$\begin{aligned}
& y=\left(\frac{d y}{d x}\right) x+\frac{4}{\left(\frac{d y}{d x}\right)} \\
& \therefore y\left(\frac{d y}{d x}\right)=\left(\frac{d y}{d x}\right)^2 x+4
\end{aligned}$
Asked in: MHT CET 2021 (22 Sep Shift 1)
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