hey put x=sinu and y=sinv
differentiate u'll get it........
Form the differential equation satisfied by [1 – x2]1/2 + [1 – y2]1/2 = a.(x – y), a is an arbitrary
constant.
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2 Answers
MATRIX
·2009-03-20 08:20:40
substituting..............
u'll get.........
(1-sin2u)1/2+(1-sin2v)1/2=a(sinu-sinv)
cosu+cosv=a(sinu-sinv).......
a=cosu+cosv/sinu-sinv
a=(2.cos(u+v)/2.cos(u-v)/2)/(2.cos(u+v)/2.sin(u-v)/2)
=cot((u-v)/2)
we can write.......
u-v/2=cot-1a........
sin-1x-sin-1y=cot-1a
Differentiating.........
1/(1-x2)1/2=1/(1-y2)1/2dy/dx
dy/dx=(1-y2)1/2/(1-x2)1/2
Got it!!!!!!!!