Question

The degree of D.E ${[5+{\left(\frac{dy}{dx}\right)}^2]}^{5/3}=7\left(\frac{d^{2}y}{d{x}^2}\right)$

• A. $1$
• B. $4$
• C. $3$
• D. $2$

Answer 1

Answer: (C)

$3$

${[5+{\left(\frac{dy}{dx}\right)}^2]}^{5/3}=7\left(\frac{d^{2}y}{d{x}^2}\right)$

$⟹{[5+{\left(\frac{dy}{dx}\right)}^2]}^5={\left[7\left(\frac{d^{2}y}{d{x}^2}\right)\right]}^3$ ..... Taking cube on both sides

${[5+{\left(\frac{dy}{dx}\right)}^2]}^5=7^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^3$

Order is the highest numbered derivative, while degree is the highest power of the highest order derivative.

$\therefore$ Order $=2$ and Degree $=3$