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Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 38 maths textbook solution.

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Answer : (c)\; \log\; x

Hint: The given differential equation is linear in y.

Given : (x \log x) \frac{d y}{d x}+y=2 \log x

Explanation: Divide on both sides by x \log x

\Rightarrow \frac{d y}{d x}+y\left(\frac{1}{x \log x}\right)=\frac{2}{x}

The equation is linear in y

\begin{aligned} &I F=e^{\int \frac{1}{x \log x} d x} \\ &\text { Let } \log x=t \Rightarrow \frac{1}{x} d x=d t \\ &I F=e^{\int \frac{1}{t} d t}=e^{\log t}=t \\ &I F=\log x \end{aligned}

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