Solve the differential equation:

Solve the following initial value problem:
(1 + x y) y dx + (1 – x y) x dy = 0, y (1) = 1.

154. Find the particular solution of the differential equation
(1 + e^2x ) dy + (1 + y² ) e^x dx = 0, given that y = 1 when x = 0.

Solve the differential equation;
x (1 + y² ) dx – y (1 + x² ) dy = 0  given that y = 0 when x = 1. 

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2 x² + 1) dx (x ≠ 0).