The sum of order and degree of differential equation $2\sqrt{\frac{d^2y}{dx^2}}+(\frac{dy}{dx})^3=0$ is:
Answer & explanation
Correct answer: option 2
Given differential equation
$2\sqrt{\frac{d^2y}{dx^2}}+\left(\frac{dy}{dx}\right)^3=0$
Remove radical to define degree
$2\sqrt{\frac{d^2y}{dx^2}}=-\left(\frac{dy}{dx}\right)^3$
Square both sides
$4\frac{d^2y}{dx^2}=\left(\frac{dy}{dx}\right)^6$
Highest order derivative is $\frac{d^2y}{dx^2}$
Order $=2$
Power of highest order derivative is $1$
Degree $=1$
Sum of order and degree
$=2+1=3$
The required sum is $3$.