p and q are positive integers and n < r < m . If the order and degree of the differential equation ( d^m y d x^m + d^n y d x^n )^ p / q =5 d^r y d x^r are respectively 4 and 3 , then

Step-by-step solution

Given ( d^m y d_x m + d^n y d_x n )^ p q =5 d^x y d_x r with order 4 and degree 3 . ( d^m y d_x m + d^x y d_x n )=5^q ( d^r y d_x r )^q Here, m>r>x . there d^m y d_x n will be the higher order operator So, m =4 Now, d^m y d_x m has a power 3 . Then, P =3 .