" 15."(dy)/(dx)=(x)/(2y+x)

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

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

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

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

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

(dy)/(dx)-(2y)/(x)=y^(4)

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

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

The solution of differential equation x^(2)=1+((x)/(y))^(-1)(dy)/(dx)+(((x)/(y))^(-2)((dy)/(dx))^(2))/(2!)+(((x)/(y))^(-3)((dy)/(dx))^(3))/(3!)