The integrating factor of the differential equation x dy dx + 2y = x^2 x is

Step-by-step solution

The given differential equation is x dy dx + 2y = x^2 x . Dividing the entire equation by x , we get: dy dx + 2 x y = x x This is a linear differential equation of the form dy dx + Py = Q , where P = 2 x and Q = x x . The integrating factor (IF) is given by e^ P dx . IF = e^ 2 x dx IF = e^ 2 x IF = e^ x^2 IF = x^2 Answer: x^2