If order and degree of the differential equation ( d ^2 y ~d x^2 )^5+4 ( ~d ^2 y ~d x^2 )^5 ( ~d ^3 y ~d x^3 ) + d ^3 y ~d x^3 = x , are m and n respectively, then the value of (m^2+n^2 ) is equal to

Step-by-step solution

Given differential equation is ( d ^2 y ~d x^2 )^5+4 ( ~d ^2 y ~d x^2 )^5 ~d ^3 y ~d x^3 + d ^3 y ~d x^3 = x ( d ^2 y ~d x^2 )^5 ~d ^3 y ~d x^3 +4 ( ~d ^2 y ~d x^2 )^5+ ( d ^3 y ~d x^3 )^2= x ~d ^3 y ~d x^3 Here, order =3 and degree =2 aligned & m=3, n=2 & m^2+n^2=3^2+2^2=13 aligned