" 4."(x-x^(3))(dy)/(dx)+(2x^(2)-1)y=ax^(3)

The solution of 3x(1-x^(2))y^(2)(dy)/(dx)+(2x^(2)-1)y^(3)=ax^(3) is

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

(dy)/(dx)=(3x+y+4)^(2)

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

For each of the following differential equations verify that the accompanying functions a solution.Differential Function x(dy)/(dx)=yy=axx+y(dy)/(dx)=0y=+-sqrt(a^(2)-x^(2))x(dy)/(dx)y=y^(2)y=(a)/(x+a)x^(3)(d^(2)y)/(dx^(2))=1y=ax+b+(1)/(2x)y=((dy)/(dx))^(2)y=(1)/(4)(x+-a)^(2)

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

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

x^(2) y -x^(3) (dy)/(dx) = y^(4) cos x rArr x^(3) y^(-3) =

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

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