Method of Differentiation
Implicit Differentiation
Premium Question
Grade 12
Question:
If $y = e^{3 \sin^{-1} x}$ and $(1 - x^2)y'' - xy' = ky$, the value of $k$ equals _____.
Step-by-Step Solution
Key Concept: Differentiate $y = e^{3 \sin^{-1} x}$ once to obtain a relation of the form $\sqrt{1 - x^2} y' = 3y$, square it, and differentiate that squared relation again.
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Correct Answer: 9