urgent

Form the differential equation satisfied by [1 – x2]1/2 + [1 – y2]1/2 = a.(x – y), a is an arbitrary
constant.

2 Answers

1
MATRIX ·

hey put x=sinu and y=sinv
differentiate u'll get it........

1
MATRIX ·

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!!!!!!!!

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