WBJEE · Maths · Differential Equations
If \(\sqrt{y}=\cos ^{-1} x\), then it satisfies the differential equation \(\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=c,\) where \(c\) is equal to
- A 0
- B 3
- C 1
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
Given, \(\sqrt{y}=\cos ^{-1} x \Rightarrow y=\left(\cos ^{-1} x\right)^{2}\) On differentiating both sides w.r.t. \(x\), we get \[ \frac{d y}{d x}=2\left(\cos ^{-1} x\right) \times \frac{-1}{\sqrt{1-x^{2}}} \] Again, differentiating both sides w.r.t. \(x\), we get…
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