Question

What is the degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{3/2}={\left(\frac{d^{2}y}{d{x}^2}\right)}^2$?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

Given differential equation should contain integral powers,

${\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{3}{2}}={\left(\frac{d^{2}y}{d{x}^2}\right)}^2⟹{\left(\frac{d^{3}y}{d{x}^3}\right)}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$

$\therefore$ the power of the order in the differential equation is the degree of the differential equation which is $3$.