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JEE Mains · Maths · STD 12 - 9. differential equations
Let a curve \(y=f(x)\) pass through the point \(\left(2,\left(\log _{e} 2\right)^{2}\right)\) and have slope \(\frac{2 y}{x \log _{e} x}\) for all positive real value of \(x\). Then the value of \(f(e)\) is equal to \(.....\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(y^{\prime}=\frac{2 y}{x \ell n x} \Rightarrow \frac{d y}{d x}=\frac{2 y}{x \ln x}\) \(\Rightarrow \frac{d y}{y}=\frac{2 d x}{x \ell n x}\) \(\Rightarrow \ell n|y|=2 \ell n|\ell n x|+C\) \(\text { Put } x=2, y=(\ell n 2)^{2}\)…
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