Question

The order and degree of the 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. $1,2$
• D. $3,3$

Answer 1

The correct option is D $3,3$

${(1+3\frac{dy}{dx})}^{2/3}=4\frac{d^{3}y}{{dx}^3}\Rightarrow {(1+3\frac{dy}{dx})}^2=16{\left(\frac{d^{3}y}{{dx}^3}\right)}^3$
Highest derivative is third order
And power of highest order derivative is 3
Hence order is 3 and degree is 3