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Question : 33
Total: 50
If y = s i n ( m s i n − 1 x )
Solution: 👈: Video Solution
Given, y = s i n ( m ( s i n − 1 x ) ) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ( i )
Differentiating both sides w.r.t.x
= cos ( m s i n − 1 x ) ×
⇒
=
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ( i i )
⇒ ( √ 1 − x 2 ) y ′ =
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ( i i i )
⇒ ( √ 1 − x 2 ) y ′ = m cos ( m s i n − 1 x )
Differentiating again w.r.t. 'x
y ′ ′ ( √ 1 − x 2 ) + y ′
= − m 2 s i n ( m s i n − 1 x )
⇒ y ′ ′ ( 1 − x 2 ) − x y ′ = − m 2 y
⇒ y ′ ′ ( 1 − x 2 ) − x y ′ + m 2 y = 0
or, ( 1 − x 2 )
− x
+ m 2 y = 0
Differentiating both sides w.r.t.
Differentiating again w.r.t. '
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