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  • Please Solve R.D.Sharma class 12 Chapter 21 Differential Equations Exercise 21.9 Question 4 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 21  Differential Equations Exercise 21.9 Question 4 Maths textbook Solution.

Answers (1)

Answer: y=xlog|x|+cx

Given: here ,x\frac{dy}{dx}=x+y

To find: we have to find the solution of given differential equation.

Hint: in homogeneous differential equation

Put y=vx and \frac{dy}{dx}=v+x\frac{dv}{dx}

Solution: we have,

x\frac{dy}{dx}=x+y

\Rightarrow \frac{dy}{dx}=\frac{x+y}{x}

Clearly It is homogeneous equation

Put y=vx\Rightarrow \frac{dy}{dx}=v+\frac{xdv}{dx}

So,

   \begin{aligned} &v+x \frac{d v}{d x}=\frac{x+v x}{x} \\ &\Rightarrow v+x \frac{d v}{d x}=\frac{x(1+v)}{x} \\ &\Rightarrow x \frac{d v}{d x}=1+v-v \\ &\Rightarrow x \frac{d v}{d x}=1 \\ &\Rightarrow \int d v=\int \frac{1}{x} d x \\ &\Rightarrow v=\log x+c \\ &\Rightarrow \frac{y}{x}=\log x+c \\ &\Rightarrow y=x \log x+c x \end{aligned}

    This is required solution.

Posted by

infoexpert21

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