Solve the differential equation : `(1 + y^2) (1 + log x)dx + x dy = 0` given that `y = 1 when x = 1`

Solve the differential equation : x (1 + y^2) dx - y (1 + x^2) dy = 0 given that y = 0 when x = 1

Solve the differential equation : (1 + e^(2x))dy + (1 + y^2)e^(2x) dx = 0 given that y = 1 when x = 0

Solve the differential equation : x (dy/dx) + y = x log x

Solve the differential equation (1 + y^2) dx − (tan^(−1) y − x) dy = 0

Solve the differential equation : x^2 (y + 1) dx + y^2 (x - 1) dy = 0

Solve the differential equation : x^2 (y + 1) dx - y^2 (x - 1) dy = 0

Solve the differential equation ( x+ y ) ( dy)/( dx) = 1

Find a particular solution of the differential equation (x-y)(dx+dy) = dx - dy given that y = -1 when x = 0