The order and degree of a differential equation obtained by eliminating arbitrary constant $C$ from the…
- 1,3
- 1,4
- 1,1
- 1,2
Solution
from (i) and (ii)
$\begin{aligned} & y^2=2 y \frac{\mathrm{d} y}{\mathrm{~d} x}\left(x+\sqrt{y \frac{\mathrm{d} y}{\mathrm{~d} x}}\right) \\ & \Rightarrow y-2 x \frac{\mathrm{d} y}{\mathrm{~d} x}=2 \frac{\mathrm{d} y}{\mathrm{~d} x} \cdot \sqrt{y \cdot \frac{\mathrm{d} y}{\mathrm{~d} x}} \\ & \Rightarrow\left(y-2 x \frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2=4 y\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^3 \text { order }=1, \text { degree }=3\end{aligned}$Asked in: MHT CET 2022 (10 Aug Shift 1)