JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y^{1 / 4}+y^{-1 / 4}=2 x\), and \(\left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+\alpha x \frac{d y}{d x}+\beta y=0\) then \(|\alpha-\beta|\) is equal to ...... .
- A \(17\)
- B \(18\)
- C \(19\)
- D \(20\)
Answer & Solution
Correct Answer
(A) \(17\)
Step-by-step Solution
Detailed explanation
\(y^{\frac{1}{4}}+\frac{1}{y^{\frac{1}{4}}}=2 x\) \(\Rightarrow\left(y^{\frac{1}{4}}\right)^{2}-2 x y^{\left(\frac{1}{4}\right)}+1=0\) \(\Rightarrow y^{\frac{1}{4}}=x+\sqrt{x^{2}-1} \text { or } x-\sqrt{x^{2}-1}\) So,…
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