JEE Mains · Maths · STD 12 - 9. differential equations
If the curve \(y = f(x)\) passes through the point \((1, e)\) and satisfies the differential equation \(dy = y(2 + \log_e x)\,dx\), \(x > 0\), then \(f(e)\) is equal to :
- A \(e^e\)
- B \(e^{e^2}\)
- C \(e^{2e}\)
- D \(e^{2e}\)
Answer & Solution
Correct Answer
(C) \(e^{2e}\)
Step-by-step Solution
Detailed explanation
Given differential equation is \(\dfrac{dy}{y} = (2 + \log_e x) dx\) Integrating both sides, we get: \(\int \dfrac{dy}{y} = \int (2 + \log_e x) dx\) \(\log_e y = 2x + x \log_e x - x + C\) \(\log_e y = x + x \log_e x + C\) Since the curve passes through \((1, e)\), substitute…
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