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`.

Find the particular solution of the differential equation (1-y^2)(1+logx)dx+2x ydy=0, given that y=0 when x=1.

Find the particular solution of the differential equation: (1+e^2x)dy+(1+y^2)e^xdx=0 , given that y(0)=1

Find the particular solution of the differential equation (dy)/(dx)=e^x when it is given that y=1 for x=0.

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

Find the particular solution of the differential equation {xsin^(2)(y/x)-y}dx+xdy=0 , it being given that y=pi/4 when x=1 .

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

Find the particular solution of the differential equation (xe^(y//x)+y)dx=xdy , given that y(1)=0 .

Find the particular solution of the differential equation x(x^(2)-1)(dy)/(dx) =1, it being given that y = 0 when x = 2.

Find the particular solution of the differential equation ;(x^(2)+xy)dy=(x^(2)+y^(2))dx given that y=0 when x=1