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

Question

amistre64 · Answer

looks quite seperable to me ....

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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 ]

amistre64 · Answer

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

anonymous · Answer

no probs ..thanku :)

amistre64 · Answer

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