Question

The degree and order of the differential equation \(\rm (\frac{d^3y}{dx^3})^2 -(\frac{d^2y}{dx^2})^3+(\frac{dy}{dx})^4-y^5=0\)
1. 2 and 3
2. 1 and 2
3. 5 and 1
4. 4 and 3

Answer 1

Correct Answer - Option 1 : 2 and 3

Concept:

Order: The order of a differential equation is the order of the highest derivative appearing in it.

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

 

Calculation:

Given differential equation: \(\rm (\frac{d^3y}{dx^3})^2 -(\frac{d^2y}{dx^2})^3+(\frac{dy}{dx})^4-y^5=0\)

Here, highest derivative = \(\rm \frac{d^3y}{dx^3}\)

So, the order of the given DE is 3

And the power of the highest derivative (i.e., \(\rm \frac{d^3y}{dx^3}\)) is 2

∴ Degree = 2 and Order = 3

Hence, option (1) is correct.