An integrating factor of the differential equation (1-x^2 ) d y d x +x y= x^4 (1+x^5 ) ( 1-x^2 )^3 is

Step-by-step solution

Given differential equation can be rewritten as aligned & d y d x + x y 1-x^2 = x^4 ( 1-x^2 )^3 (1+x^5 ) (1-x^2 ) & d y d x + x y 1-x^2 = x^4 1-x^2 (1+x^5 ) aligned On comparing by linear differential equation is aligned d y d x +P y & =Q P & = x 1-x^2 aligned aligned IF =e^ P d x & =e^ x 1-x^2 d x & =e^ - 1 2 -2 x 1-x^2 d x =e^ - 1 2 (1-x^2 ) & =e^ (1-x^2 )^ -1 / 2 = 1 1-x^2 aligned