Get Answers to all your Questions

Name: Provide Solution For R.D. Sharma Maths Class 12 Chapter 21 Differential Equations Exercise 21.9 Question 24 Maths Textbook Solution.
Uploaded: Wed, 2021-08-25 21:27
Description: Provide Solution For R.D. Sharma Maths Class 12 Chapter 21 Differential Equations Exercise 21.9 Question 24 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 21 Differential Equations Exercise 21.9 Question 24 Maths Textbook Solution.

Answers (1)

Answer: $\frac{x^{2}}{y^{2}}\left \{ \left ( \frac{x}{y} \right )-\frac{1}{2} \right \}+logy^{2}=c$

Given: $xylog \left ( \frac{x}{y} \right )dx+\left \{ y^{2}-x^{2}log\left ( \frac{x}{y} \right ) \right \}dy=0$

To solve:We have to solve the given differential equation

Hint: $\left ( 1 \right )$ Put $y=vx$ and $\frac{dy}{dx}=v+x\frac{dv}{dx}or$

$\left ( 2 \right )$ Put $y=vx$ and $\frac{dy}{dx}=v+y\frac{dv}{dx}$

Solution: We have,

$\begin{aligned} &x y \log \left(\frac{x}{y}\right) d x+\left\{y^{2}-x^{2} \log \left(\frac{x}{y}\right)\right\} d y=0 \\ &\Rightarrow \frac{d x}{d y}=\frac{x^{2} \log \left(\frac{x}{y}\right)-y^{2}}{x y \log \left(\frac{x}{y}\right)} \end{aligned}$