Question

What is the degree of the differential equation \(\rm \left(\frac {d^3y}{dx^3}\right)^{3/2} + \left(\frac {d^2y}{dx^2}\right)^{2} = 0\) ?
1. 2
2. 4
3. 3/2
4. 1
5. 3

Answer 1

Correct Answer - Option 5 : 3

Concept:

Degree: The degree of a differential equation is the power of the highest derivative.

Calculation:

We have, \(\rm \left(\frac {d^3y}{dx^3}\right)^{3/2} + \left(\frac {d^2y}{dx^2}\right)^{2} = 0\)

⇒ \(\rm \left(\frac {d^3y}{dx^3}\right)^{3/2} = - \left(\frac {d^2y}{dx^2}\right)^{2}\)

Squaring both the sides, we get 

\(\rm \left(\frac {d^3y}{dx^3}\right)^3 = \left(\frac {d^2y}{dx^2}\right)^{4}\)

Here highest derivative is \(\rm \left(\frac {d^3y}{dx^3}\right)^3\)

∴Degree = power of \(\rm \left(\frac {d^3y}{dx^3}\right)^3\)= 3

Hence, option (5) is correct.