Question

The order and degree of differential equation ${(1+3\frac{dy}{dx})}^{2/3}=4\frac{d^{3}y}{d{x}^3}$, are

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

Answer 1

The correct option is C $3,3$

Given ${(1+3\frac{dy}{dx})}^{2/3}=4\frac{d^{3}y}{d{x}^3}$

On taking cube on both sides, we get
${(1+3\frac{dy}{dx})}^2={\left(4\frac{d^{3}y}{d{x}^3}\right)}^3$

Now,

Order: Order of a differential equation is the order of the highest order derivative (also known as differential coefficient) present in the equation

Here Order is $3$

Degree: The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

Here Degree is $3$