Question

The order and degree of the differential equation $\frac{d^{3}y}{d{x}^3}+4\sqrt{{\left(\frac{dy}{dx}\right)}^3+y^2}=0$ are respectively

• A. 3 and 2
• B. 2 and 3
• C. 3 and 3
• D. 3 and 1

Answer 1

The correct option is A 3 and 2

Making the given differential equation free of radicals we get

${\left(\frac{d^{3}y}{d{x}^3}\right)}^2={(-4\sqrt{{\left(\frac{dy}{dx}\right)}^3+y^2})}^2$

${\left(\frac{d^{3}y}{d{x}^3}\right)}^2=16[{\left(\frac{dy}{dx}\right)}^3+y^2]$

Order = Highest order derivative

= 3

Degree = exponent of highest order derivative

= 2