MHT CET · Maths · Differential Equations
The integrating factor of the differential equation \(\frac{d y}{d x}(x \log x)+y=4 \log x\) is
- A \(\log (\log x)\)
- B \(x\)
- C \(e^{x}\)
- D \(\log x\)
Answer & Solution
Correct Answer
(D) \(\log x\)
Step-by-step Solution
Detailed explanation
We have \(\frac{d y}{d x}(x \log x)+y \quad=4 \log x\)
\(\therefore \frac{d y}{d x}+\left(\frac{1}{x \log x}\right) y=\frac{4}{x}\)
\(\therefore\) I.F. \(=e^{\int \frac{d x}{x \log x}}=e^{\log (\log x)}=\log x\)
\(\therefore \frac{d y}{d x}+\left(\frac{1}{x \log x}\right) y=\frac{4}{x}\)
\(\therefore\) I.F. \(=e^{\int \frac{d x}{x \log x}}=e^{\log (\log x)}=\log x\)
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