If `x^(3)=y^(4)` prove that `(x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)`

If y=sqrt(1+sqrt(1+x^(4))), prove that y(y^(2)-1)(dy)/(dx)=x^(3)

If y = sqrt(1+sqrt(1+x^(4))) , prove that y * (y^(2) - 1)(dy)/(dx) = x^(3) .

(a) If y=cos(msin^(-1)x) prove that (1-x^(2))y_(3)-3xy_(2)+(m^(2)-1)y_(1)=0 (b) Find y'' if x^(4)+y^(4)=16 .

If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)/(3!)-y^(4)/(4!)+...

Prove that : If (4.44)^x=(0.444)^y=1000 , then prove that (1)/(x)-(1)/(y)=(1)/(3) .

If" " x^(2) + y^(2) = 1, "show that, "(3x - 4x^(3))^(2) + (3y - 4y^(3))^(2) = 1.

Prove that: 4|(x,y),(3x,0)|=3|(x,0),(5x,-4y)|

If a circle cuts the rectangular hyperbola xy = 1 in the points (x_(r), y_(r)), r = 1, 2, 3, 4 prove that x_(1), x_(2),x_(3), x_(4) = y_(1), y_(2), y_(3), y_(4) = 1

If y = sqrt(1+sqrt(1+x^4)) , prove that y(y^2-1)dy/dx = x^3

(x+y)/(2)-(x-y)/(3)=8,(x+y)/(3)+(x-y)/(4)=4