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If x 2 + y 2 =1, then : (A) yy'" - 2(y ' ) 2 +1=0 (B) yy'' + (y ' ) 2 +1=0 (C) yy " = (y ' ) 2 -1=0 (D) yy''+2(y ' ) 2 +1=0

If x2+ y2=1, then :
(A) yy'" - 2(y ' )2+1=0                                  (B) yy'' + (y ' )2+1=0
(C) yy " = (y ' )2-1=0                                   (D) yy''+2(y ' )2+1=0

Grade:12

2 Answers

AskIITian Expert Priyasheel - IITD
8 Points
13 years ago

x^2 + y^2 = 1,

Differentiate w.r.t. x,

2x + 2yy' = 0,

Again differentiate,

2 + 2( yy'' +y'^2) = 0,

or, yy'' + y'^2 + 1 = 0,

ANS is (B).

Sudheesh Singanamalla
114 Points
12 years ago

differnciating x^2 + y^2 w.r.t.  x we get

2x + 2yy' = 0  or x + yy' = 0

again differenciating w.r.t x we get

1+y'y' + yy'' = 0 or 1 + (y')^2 + yy'' = 0

so answer is (B)

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