Question

Order and degree of the differential equation, ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{3}{2}}+{\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{-2}{3}}=0$ are respectively

• A. $2,9$
• B. $3,6$
• C. $3,4$
• D. $3,13$

Answer 1

The correct option is D $3,13$

Given $(\frac{d^{3}y}{d{x}^3}{)}^{\frac{3}{2}}=-(\frac{d^{3}y}{d{x}^3}{)}^{\frac{-2}{3}}$

Raising both sides to the power 6,

$(\frac{d^{3}y}{d{x}^3}{)}^9=(\frac{d^{3}y}{d{x}^3}{)}^{-4}$

Multiplying both sides by $(\frac{d^{3}y}{d{x}^3}{)}^4$,

$(\frac{d^{3}y}{d{x}^3}{)}^{13}=1$

$⟹$ Order $=$ 3 and Degree $=$ 13