CBSE Class 12 Math 2022 Term I Solved Paper

Question : 33

Total: 50

If y=sin‌(msin‌−1x), then which one of the following equations is true?

Solution: 👈: Video Solution

Given, y=sin‌(m(sin‌−1x))‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
Differentiating both sides w.r.t. x , we get
‌

‌=cos(msin‌−1x)×‌

√1−x2

⇒‌‌‌

‌=‌

m‌cos(msin‌−1x)

√1−x2

‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
⇒‌‌(√1−x2)y′‌=‌

m‌cos(msin‌−1x)

√1−x2

‌‌‌⋅⋅⋅⋅⋅⋅⋅(iii)
⇒‌‌(√1−x2)y′=m‌cos(msin‌−1x)
Differentiating again w.r.t. ' x ', we get
y′′(√1−x2)+y′‌

(−2x)

2√1−x2

‌ =‌−m2sin‌(msin‌−1x)‌

√1−x2

⇒‌‌y′′(1−x2)−xy′=−m2y
⇒y′′(1−x2)−xy′+m2y=0
‌ or, ‌‌‌(1−x2)‌

d2y

dx2

−x‌

+m2y=0

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