`(dy)/(dx)+(2)/(x)y=3x^(2)y^((4)/(3)), x>0`

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

x(dy)/(dx)+y=3x^(2)-2,x>0

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

3x^(2)y+(dy)/(dx)=0

Solve (dy)/(dx)+2*(y)/(x)=(y^(3))/(x^(3))

(dy)/(dx)=(x+y+1)/(2x+2y+3)

(dy)/(dx)=(x+y+7)/(2x+2y+3)

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

If y=x log((x)/(a+bx)), thenx ^(3)(d^(2)y)/(dx^(2))= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^(2)y(dy)/(dx)-x(d)(y(dy)/(dx)-x)^(2)

The solution of the differential equation x=1+xy(dy)/(dx)+(x^(2)y^(2))/(2!)((dy)/(dx))^(2)+(x^(3)y^(3))/(3!)((dy)/(dx))^(3)+...is