Question

The solution of differential equation $(1 + x)y dx + (1 - y)x\, dy = 0$ is

• A. $\log_e(xy) + x - y = C$
• B. $\log_e (\frac {x} {y})+ x + y = C$
• C. $\log_e (\frac {x} {y})- x + y = C$
• D. $\log_e (xy)- x + y = C$

Answer 1

Answer: (C)

Given, $(1 + x)y \,dx + (1 - y)x \,dy = 0$
$\Rightarrow \frac{\left(1-y\right)}{y}dy+\frac{\left(1+x\right)dx}{x} = 0$
$\Rightarrow \int \left(\frac{1}{y}-1\right)+\left(\frac{1}{x}+1\right)dx=0$
$\Rightarrow log \,y - y + log \,x = C$
$\Rightarrow log\, \left(xy\right) + x - y = C$