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  • Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 12 textbook solution.

Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 12 textbook solution.

Answers (1)

Answer : \text { (a) } y=x e^{x+c}

Hint: Use variable separable method i.e. take the y terms in one side and x terms in the other.

Given : \frac{d y}{d x}-\frac{y(x+1)}{x}=0

Explanation : \frac{d y}{d x}=\frac{y(x+1)}{x}

\begin{aligned} &\frac{d y}{y}=d x\left(\frac{x+1}{x}\right) \\ &\frac{d y}{y}=\left(1+\frac{1}{x}\right) d x \end{aligned}

Integrate both sides

\begin{aligned} &\log y=x+\log x+C \\ &\log y-\log x=x+C \\ &\log \frac{y}{x}=x+C \end{aligned}

Take exponential both sides we get

\begin{aligned} &\frac{y}{x}=e^{x+c} \\ &y=x e^{x+C} \end{aligned}

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