MHT CET · Maths · Differential Equations
The integrating factor of the differential equation \(x \frac{\mathrm{dy}}{\mathrm{d} x}+\mathrm{y} \log x=x \mathrm{e}^x \cdot x^{\frac{-1}{2}} \log x(x>0)\) is
- A \((\log x)^x\)
- B \(x^{\log x}\)
- C \((\sqrt{x})^{\log x}\)
- D \(\mathrm{e}^{\sqrt{x} \log x}\)
Answer & Solution
Correct Answer
(C) \((\sqrt{x})^{\log x}\)
Step-by-step Solution
Detailed explanation
Divide by \(x\): \(\frac{\mathrm{dy}}{\mathrm{d} x} + \frac{\log x}{x} \mathrm{y} = \mathrm{e}^x \cdot x^{\frac{-1}{2}} \log x\) \(P(x) = \frac{\log x}{x}\)
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