Question

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

Answer 1

looks quite seperable to me ....

Answer 2

how do we solve it though..
yup its separable but stuck up after the first step

Answer 3

1/sqrt(1-a^2) maybe try some trig substitutions?

Answer 4

tried ...i get the integrated form of the answer but not able to reach final conclusion

Answer 5

hmm, let sin(u) = x, cos(u) du = dx
...sin(v) = y, cos(v) = dv

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

cos^2(v)du+cos^2(u)dx

sec^2(u)du= -sec^2(v) dv

isnt tan the integral of sec^2?

tan(u)= -tan(v) + C

u= arctan[ -tan(v) + C ]

Answer 6

arcsin(x)= arctan[ -tan(arcsin(y)) + C ]

x= sin {arctan[ -tan(arcsin(y)) + C ] }

might need to draw some pictures to look thru the trig parts

Answer 7

no probs ..thanku :)

Answer 8

youre welcome ... thats my idea at least :) good luck