Question

The order and degree of the differential equation

$\frac{d^{2}y}{dx^{2}} + \left( \frac{dy}{dx} \right)^{\frac{1}{3}} + x^{\frac{1}{4}} = 0$, are respectively

• A. 2, 3
• B. 3, 3
• C. 2, 6
• D. 2, 4

Answer 1

Answer: (A)

2, 3

Answer 2

The highest order derivative involved is $\frac{d^{2}y}{dx^{2}}$which is the 2^nd order derivative. Hence order of the differential equation is 2. Making the above equation free from radical, as far as the derivatives are concerned, we have

$\left( \frac{d^{2}y}{dx^{2}} + x^{\frac{1}{4}} \right)^{3} = - \frac{dy}{dx}$ i.e. $\left( \frac{d^{2}y}{dx^{2}} + x^{\frac{1}{4}} \right)^{3} + \frac{dy}{dx} = 0$

The exponent of highest order derivative $\frac{d^{2}y}{dx^{2}}$will be 3. Hence degree of the differential equation is 3.