(y^(2)+(3)/(2))(y^(2)-(3)/(2))

Solution (1+x sqrt(x^(2)+y^(2)))dx+y(-1+sqrt(x^(2)+y^(2)))dy=0 is x-(y^(2))/(2)+(1)/(3)(x^(2)+y^(2))^((3)/(2))+c=0

Add the following algebraic expressions: 2,(2y)/(3)-(5y^(2))/(3)+(5y^(3))/(2),-(4)/(3)+(2y^(2))/(3)-(y)/(2),(5y^(3))/(3)+3y^(2)+3y+(6)/(5)

the solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2))/(y(y^(2)+3x^(2)))=0 is

The value of ((x-y)^(3)+(y-z)^(3)+(z-x)^(3))/((x^(2)-y^(2))^(3)+(y^(2)-z^(2))^(3)+(z^(2)-x^(2)backslash)^(3)) is (b) 1( c) [2(x+y+z)]^(-1)(d)[(x+y)(y+z)(z+x)]^(-1)

The solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0 is (a) x^(4)+y^(4)+x^(2)y^(2)=c (b) x^(4)+y^(4)+3x^(2)y^(2)=c (c) x^(4)+y^(4)+6x^(2)y^(2)=c (d) x^(4)+y^(4)+9x^(2)y^(2)=c

y^(3)-y=2x, provethat (d^(2)y)/(dx^(2))=(-24y)/((3y^(2)-1)^(3))

If y^(3)-y=2x, prove that (d^(2)y)/(dx^(2))=-(24y)/((3y^(2)-1)^(3))

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

Find ((x^(2)-y^(2))^(3) + (y^(2) -z^(2))^(3)+ (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))