Degree of Differential Equations

If a differential equation is expressible in a polynomial form, then the integral power of the highest order derivative that appears is called the degree of the differential equation. The degree of the differential equation is the power of the highest ordered derivative present in the equation. To find the degree of the differential equation, we need to have a positive integer as the index of each derivative.

Example:

 (dy/dx4) 3 + 4(dy / dx)7+6y
  = 5cos3x(dy/dx4)3+ 4 (dy / dx)7+6y=5cos3x

Here the order of the differential equation is 4 and the degree is 3.

Note: If a differential equation is not expressible in terms of a polynomial equation having the highest order derivative as the leading term, then that degree of the differential equation is not defined.