Question

The order and degree of the differential equation ${(1+3\frac{dy}{dx})}^{\frac{2}{3}}=4\left(\frac{d^{3}y}{d{x}^3}\right)$ is:

• A. $1,\frac{2}{3}$
• B. $3,1$
• C. $3,3$
• D. $1,2$

Answer 1

The correct option is C $3,3$

Given, differential equation as $1+3{\left(\frac{dy}{dx}\right)}^{\frac{2}{3}}=4\frac{d^{3}y}{d{x}^3}$
On cubing the equation on both the sides,
${\left(\right(1+3{\left(\frac{dy}{dx}\right)}^{\frac{2}{3}})}^3={\left(4\frac{d^{3}y}{d{x}^3}\right)}^3$
$\Rightarrow {(1+3\frac{dy}{dx})}^2=64\times {\left(\frac{d^{3}y}{d{x}^3}\right)}^3$

The order of the equation is the highest degree of differential in the equation.
Here it is $3$....... (since $\frac{d^{3}y}{d{x}^3}$ exists in the equation)
$\therefore$ Order $=3$
The degree of the equation is the power of the highest order differential term in the equation.
Here, it is $3$........ (since power of $\frac{d^{3}y}{d{x}^3}$ in the equation is $3$)
$\therefore$ Degree $=3$