JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\frac{1}{ x ^{2}-1} y =\left(\frac{ x -1}{ x +1}\right)^{\frac{1}{2}}\), \(x>1\) passing through the point \(\left(2, \sqrt{\frac{1}{3}}\right)\). Then \(\sqrt{7} y (8)\) is equal to.
- A \(11+6 \log _{ e } 3\)
- B \(19\)
- C \(12-2 \log _{ e } 3\)
- D \(19-6 \log _{ e } 3\)
Answer & Solution
Correct Answer
(D) \(19-6 \log _{ e } 3\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\frac{1}{x^{2}-1} y=\left(\frac{x-1}{x+1}\right)^{\frac{1}{2}}\) \(\frac{d y}{d x}+P y=Q\) \(I \cdot F .= e ^{\int Pdx }=\left(\frac{ x -1}{ x +1}\right)^{\frac{1}{2}}\) \(y\left(\frac{x-1}{x+1}\right)^{\frac{1}{2}}=\int\left(\frac{x-1}{x+1}\right)^{1} d x\)…
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