The order and degree of the differential equation $\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$ are…
The order and degree of the differential equation $\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$ are respectively
- 1 and $\frac{1}{2}$
- 2 and 1
- 1 and 1
- 1 and 2
Solution
$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$ or
$
\sqrt{\frac{d y}{d x}}=4 \frac{d y}{d x}+7 x
$
Squaring both side,
$
\begin{aligned}
\frac{d y}{d x} & =16\left(\frac{d y}{d x}\right)^2+49 x^2+56 x \frac{d y}{d x} \\
\therefore \text { Order } & =1 \text { and degree }=2
\end{aligned}
$
$\because$ highest order derivative is $\left(\frac{d}{d x}\right)$ and its exponent is 2
Asked in: AP EAMCET 2021 (23 Aug Shift 1)
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