`y-x(dy)/dx= x+y(dy)/dx`

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Solve : y^(2)-x(dy)/(dx)=a(y+(dy)/(dx))

x(dy)/(dx)=y

y^(2)-x^(2) (dy)/(dx) = xy(dy)/(dx)

Solution of differential equation y-x(dy)/(dx)=y^(2)+(dy)/(dx), when x=1,y=2, is

y^(2)+x^(2)(dy)/(dx)=xy(dy)/(dx)

a(x(dy)/(dx)+2y)=xy(dy)/(dx)

General solution of differential equation x^(2)(x+y(dy)/(dx))+(x(dy)/(dx)-y)sqrt(x^(2)+y^(2))=0 is

y^(3) - (dy)/(dx) =x^(2) (dy)/(dx)

(dy)/(dx)=(x+y)/(x-y)

Solution of the differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx))=(x sin^(2)(x^(2)+y^(2)))/(y^(3))