Xy dx + (1+x^2) dy =0

(1 + x^2) dy = - xy dx
dy/dx = -xy/(1+x^2)
y = ʃ -xy/(1+x^2) dx
y = -y ʃ x/(1+x^2) dx
-1 = ʃ x(1+x^2)^-1 dx
-1 = ʃ 1/2 (1+x^2)^-1 d(1+x^2)
-1 = 1/2 ln 1+x^2
-2 = ln (1+x^2)
ln e^-2 = ln (1+x^2)
e^-2 = 1+x^2

x = √ (1/e^2 -1)
x = √ ((1-e^2)/e^2)
x = 1/e √(1 -e^2)