AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(x \log x d y=(x \log x-y) d x\) is
- A \((x-y) \log x+x=c\)
- B \(x-y=\frac{x}{\log x}+c\)
- C \(y-x=\frac{x}{\log x}+c\)
- D \((y-x) \log x+x=c\)
Answer & Solution
Correct Answer
(D) \((y-x) \log x+x=c\)
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx} + \frac{1}{x \log x} y = 1 \) IF \( = e^{\int \frac{1}{x \log x} dx} = e^{\log (\log x)} = \log x \) \( y (\log x) = \int 1 \cdot (\log x) dx + c \) \( y \log x = x \log x - x + c \) \( (y - x) \log x + x = c \)
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