" 23."x^(3)(dy)/(dx)=y^(3)+y^(2)sqrt((y^(2)-x^(2)))

The solution of the differential equation x^(3)(dy)/(dx)=y^(3)+y^(2)sqrt(y^(2)-x^(2)) is :

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))

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

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

If sqrt(1-x^(6))+sqrt(1-y^(6))=a(x^(3)-y^(3)), then prove that (dy)/(dx)=(x^(2))/(y^(2))sqrt((1-y^(6))/(1-x^(6)))

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

Solve the differential equations: x^3(dy)/(dx)=y^3+y^2sqrt(y^2-x^2),x>0

The solution of the differential equation x^3(dy)/(dx)=y^3+y^2sqrt(y^2-x^2) is :

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