Continuity and DifferentiabilityHard
Question
If y = sin(m sin-1 x), then (1 - x2) y″ - xy′ is equal to
Options
A.m2y
B.my
C.- m2y
D.None of these
Solution
y = sin(m sin-1 x) ⇒ 
= cos(m sin-1 x) 
Squaring and cross multiplying,
(1 - x2) y12 = m2 (1 - y2), Again differentiating w.r.t.x
(1 - x2) 2y1y2 + (- 2x) y12 = m2 (- 2yy1)
Dividing by 2y1,
(1 - x2) y2 - xy1 = - m2y
= cos(m sin-1 x) Squaring and cross multiplying,
(1 - x2) y12 = m2 (1 - y2), Again differentiating w.r.t.x
(1 - x2) 2y1y2 + (- 2x) y12 = m2 (- 2yy1)
Dividing by 2y1,
(1 - x2) y2 - xy1 = - m2y
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