Question

The degree of the differential equation (1 + (dy/dx)² )^3/2 = d²y/dx² is:

A. 4
B. 3/4
C. not defined
D. 2

Answer 1

Correct option is (D) 2.

In general terms for a polynomial the degree is the highest power

Now for degree to exist the given differential equation must be a polynomial in some differentials

Here differentials mean

The given differential equation is polynomial in differentials dy/dx and d²y/dx²

Degree of differential equation is defined as the highest integer power of highest order derivative in the equation

Here the highest derivative is d²y/dx² and there is only one term of highest order derivative in the equation which is (d²y/dx²)² whose power is 2 hence degree is 2