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  • Provide solution for RD Sharma Maths Class12 Chapter 21 Differential Equation exercise 21.5 question 8.

Provide solution for RD Sharma Maths Class12 Chapter 21 Differential Equation exercise 21.5 question 8.

Answers (1)

Answer: y=x \log \left | x \right |-x+C

Hint: Using by parts (ILATE) Rule having 1st function is \log x and 2nd be 1.

Given: \frac{dy}{dx}=\log x

Solution:\frac{dy}{dx}=\log x

dy=\log x\; dx

Integrate on both sides

\int dy=\int \log x\times 1

Using ILATE Rule, \left.\int f(x) g(x) d x=f(x) \int g(x) d x-\int\left(f^{\prime}(x) \int g(x) d x\right) d x\right]\begin{aligned} &y=\log x \int 1 d x-\int\left(\frac{d(\log x)}{d x} \int 1 d x\right) d x \\ &y=(\log x) x-\int \frac{1}{x} \times x d x \\ &y=x \log x-x+C \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[\int \log x=x \log x-x\right] \end{aligned}

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