Mark (√) against the correct answer in the following: The solution of the $D E x d y+y d x=0$ is A. $x+y=C$ B. $\mathrm{xy}=\mathrm{C}$ C. $\log (\mathrm{x}+\mathrm{y})=\mathrm{C}$ D. None of these

Home » Mark (√) against the correct answer in the following: The solution of the is A. B. C. D. None of these

Mark (√) against the correct answer in the following: The solution of the $D E x d y+y d x=0$ is
A. $x+y=C$
B. $\mathrm{xy}=\mathrm{C}$
C. $\log (\mathrm{x}+\mathrm{y})=\mathrm{C}$ D. None of these

CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal

Mark (√) against the correct answer in the following: The solution of the $D E x d y+y d x=0$ is
A. $x+y=C$
B. $\mathrm{xy}=\mathrm{C}$
C. $\log (\mathrm{x}+\mathrm{y})=\mathrm{C}$ D. None of these

Solution:

$\begin{array}{l} \text { Given } x d y+y d x=0 \\ x d y=-y d x \end{array}$
$-\frac{d y}{y}=\frac{d x}{d x}$
On integrating on both sides we get,
$\begin{array}{l} -\log y=\log x+c \\ \log x+\log y=c \\ \log x y=c \\ x y=c \end{array}$
Therefore $x y=c$ is the solution of $x d y+y d x=0$