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

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

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

Solve the differential equation: (1+y+x^2y)dx+(x+x^3)dy=0

Solve the differential equation x*(dy)/(dx)-y=logx .

Find the particular solution of the differential equation (1+y^(2))(1+logx)dx+xdy=0 , it is given that at x=1 , y=1 .

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

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

Solve the differential equation y^(2)(dx)/(dy) + x = 1 .

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

Solve the differential equation x(x^2-1)(dy)/(dx)=1 , given that when x=2, y=0 .