An integrating factor of the equation (1+y+x^2 y ) d x+ (x+x^3 ) d y=0 is

Step-by-step solution

Given, differential equation is, aligned & d x (1+y+x^2 y )+ (x+x^3 ) d y=0 & d y d x =- [ 1+y+x^2 y x+x^3 ] aligned aligned & d y d x =- 1 x (1+x^2 ) + (1+x^2 ) y x (1+x^2 ) & d y d x - y x =- 1 x (1+x^2 ) & aligned Here, p=- 1 2 , Q=- 1 x (1+x^2 ) aligned Integrating factor & e^ p d x & =e^ (- 1 x ) d x & =e^ - x & =e^ ( 1 x ) & = 1 x aligned