= = & gt(x^2+2x)dx+y^2dx+2ydy=0

= => (x 2+2x) e xdx+y 2exdx+2yexdy = 0 (both ends of the equation are multiplied by e x)

= = & gt(x^2+2x)e^xdx+d(y^2*e^x)=0

= = & gt∫(x^2+2x)e^xdx+∫d(y^2*e^x)=0

= =>x 2 * e x+y 2 * e x = c (c is an integer constant)

= = & gtx^2+y^2=Ce^(-x)

The general solution of this equation is x 2+y 2 = ce (-x).

6. Solution: ∫xy '+y = x3 * y6

= = & gt(xy)'=(xy)^6/x^3

= = & gtd(xy)/(xy)^6=dx/x^3

= =>-(-1/5)/(xy) 5 =-(1/2)/x2+c/10 (c is an integer constant).

= = & gt5x^3*y^5-2=Cx^5*y^5

The general solution of this equation is 5x 3 * y 5-2 = CX 5 * y 5.