WBJEE · Maths · Differential Equations
The integrating factor of the differential equation \(3 x \log _{e} x \frac{d y}{d x}+y=2 \log _{e} x\) is given by
- A \(\left(\log _{e} x\right)^{3}\)
- B \(\log _{e}\left(\log _{e} x\right)\)
- C \(\log _{e} x\)
- D \(\left(\log _{e} x\right)^{1 / 3}\)
Answer & Solution
Correct Answer
(D) \(\left(\log _{e} x\right)^{1 / 3}\)
Step-by-step Solution
Detailed explanation
Given, \(3 x \log _{e} x \frac{d y}{d x}+y=2 \log _{e} x\) Dividing both sides by \(3 x \log _{e} x,\) we get \(\frac{d y}{d x}+\frac{1}{3 x \log _{e} x} y=\frac{2 \log _{e} x}{3 x \log _{e} x}\) \(\Rightarrow \frac{d y}{d x}+\frac{1}{3 x \log _{e} x} y=\frac{2}{3 x}\) which is…
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