Question

A first-order and first-degree differential equation in variables $\mathrm{x}$ and $\mathrm{y}$ is characterized by

• A. First order of differentiation of $y$ with respect to $x$and first degree of $\frac{dy}{dx}$
• B. Order of differentiation of $y$ with respect to $x$ and power of $y$
• C. Powers of $x$ and$y$
• D. None of the above

Answer 1

The correct option is A

First order of differentiation of $y$ with respect to $x$and first degree of $\frac{dy}{dx}$

Explanation for correct option:

Explain the order and degree of differential equations in variables $\mathrm{x}$ and $\mathrm{y}$

The power of the derivative of ${\left(\frac{dy}{dx}\right)}^1$is one.

$\therefore$Degree of $\frac{\mathrm{dy}}{\mathrm{dx}}=1$

Here $y$is differentiated only one time $\frac{d}{dx}\left(y\right)$

$\therefore$Order of $\frac{\mathrm{dy}}{\mathrm{dx}}=1$

Hence, Option (A) is the correct answer.