JEE Mains · Maths · STD 12 - 9. differential equations
Let a smooth curve \(y=f(x)\) be such that the slope of the tangent at any point \((x, y)\) on it is directly proportional to \(\left(\frac{-y}{x}\right)\). If the curve passes through the point \((1,2)\) and \((8,1)\), then \(\left| y \left(\frac{1}{8}\right)\right|\) is equal to
- A \(2 \log _{ e } 2\)
- B \(4\)
- C \(1\)
- D \(4 \log _{e} 2\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} \propto \frac{-y}{x}\) \(\frac{d y}{d x}=\frac{-k y}{x} \Rightarrow \int \frac{d y}{y}=-K \int \frac{d x}{x}\) \(\ln |y|=-K \ln |x|+C\) If the above equation satisfy \((1,2)\) and \((8,1)\) \(\ln 2=-K \times 0+C \Rightarrow C=\ln 2\)…
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