​ Let y = y(x) be the solution of the differential equation [(x+2)e^(y+1/x+2)+(y+1)] dx = (x + 2) dy, y(1) = 1. If the domain of y = y(x)

Question

Let y = y(x) be the solution of the differential equation [(x+2)^{\(e^{(\frac{y+1}{x+2})}\)}+(y+1)] dx = (x + 2) dy, y(1) = 1. If the domain of y = y(x) is an open interval (α, β), then |α+β| is equal to _______.

Answer 1

Although x = –2 should be excluded from domain but according to the given problem it will the most appropriate solution.