Integrating factor of the differential equation d y d x +y= x^3+y x is

Step-by-step solution

The given differential equation is dy dx + y = x^3 + y x . Rearranging the terms to the standard linear form dy dx + P(x)y = Q(x) , we have: dy dx + y = x^2 + y x dy dx + y - y x = x^2 dy dx + y (1 - 1 x ) = x^2 Here, P(x) = 1 - 1 x . The integrating factor (IF) is given by e^ P(x) dx . IF = e^ (1 - 1 x ) dx = e^ x - |x| = e^x e^ - |x| = e^x 1 x = e^x x . Answer: e^x x