Solve the differential equation: (1 + y² )(1 + logx) dx + xdy = 0.

Solve: .

Solve .

Form the differential equation having y = (sin^-1x)² + A cos^-1x + B, where A and B are arbitrary constants, as its general solution.

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is , is given by x² – y² = cx.