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

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(1-x^(2))(dy)/(dx)-xy=1

(1-x^(2))(dy/dx)+xy=xy^(2)

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

Solve the following differential equations : (1) x^(2) (dy)/(dx)= x^(2) + xy + y^(2)

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

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

if y=(sin^(-1)x)/(sqrt(1-x^(2))), prove that (1-x^(2))(dy)/(dx)=xy+1

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

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

(1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 if x=1