6.`" "e^xdy/dx=2xy^2+y*e^x`

solve xdy/dx-y=2x^2

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

xdy-ydx=xy^(2)dx

y =x^2+(1)/(x^2 +(1)/(x^2+.....oo)) then prove that xdy/dx =(2xy^2)/(1+y^2).

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

The solution of the differential equaiton (ydx+xdy)/(ydx-xdy)=(x^(2)e^(xy))/(y^(4)) satisfying y(0) = 1 , is

Solution of xy-(dy)/(dx)=y^(3)e^(-x^(2)) is

The solution of the differential equation xdy-ydx+3x^(2)y^(2)e^(x^(3))dx=0 is (where, c is an arbitrary constant)