If the solution curve of the differential equation \(\left(y-2 \log _{\mathrm{e}} x\right)\) \(d x+\left(x \log _{\mathrm{e}} x^2\right) d y=0, x>1\) passes through the points \(\left(e, \frac{4}{3}\right)\) and \(\left(e^4, \alpha\right)\), then \(\alpha\) is equal to ______ .

[JEE Main 2023, 8 Apr (Shift 1)]

Question

If the solution curve of the differential equation \(\left(y-2 \log _{\mathrm{e}} x\right)\) \(d x+\left(x \log _{\mathrm{e}} x^2\right) d y=0, x>1\) passes through the points \(\left(e, \frac{4}{3}\right)\) and \(\left(e^4, \alpha\right)\), then \(\alpha\) is equal to ______ .

[JEE Main 2023, 8 Apr (Shift 1)]

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If the solution curve of the differential equation \(\left(y-2 \log _{\mathrm{e}} x\right)\) \(d x+\left(x \log _{\mathr…

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