Question

The order and degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+3\frac{dy}{dx}=\sqrt{x};x>0$ are ______ respectively.

• A. $2$ and $6$
• B. $3$ and $2$
• C. $2$ and $3$
• D. $2$ and degree in undefined

Answer 1

Answer: (C)

$2$ and $3$

Given differential equation is ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+3\frac{dy}{dx}=\sqrt{x}$

Order of a differential equation is the number of the highest order derivative.

Degree of a differential equation is the highest power of the highest order derivative.

Highest order derivative if second order derivative

So, order is $2$

Degree of the highest order derivative is $3$
So, degree is $3$.

Hence, option C is correct.