`dy/dx=sqrt(4-y^2)` (-2 < y < 2)

Solve the following differential equations (dy)/(dx)=sqrt(4-y^(2))

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

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

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

A normal is drawn at a point P(x,y) of a curve. It meets the x-axis at Q such that PQ is of constant length k . Answer the question:The differential equation describing such a curve is (A) y dy/dx=+-sqrt(k^2-x^2) (B) x dy/dx=+-sqrt(k^2-x^2) (C) y dy/dx=+-sqrt(k^2-y^2) (D) x dy/dx=+-sqrt(k^2-y^2)

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

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

dy/dx + sqrt(((1-y^2)/(1-x^2))) = 0

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

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