Question

The number of solutions of $\frac{dy}{dx}=\frac{y+1}{x-1}$ when $y\left(1\right)=2$ is

• A. none
• B. one
• C. two
• D. infinite

Answer 1

Answer: (B)

$\frac{dy}{dx}=\frac{y+1}{x-1}$
$\Rightarrow \frac{dy}{y+1}=\frac{dx}{x-1}$
On integration, we get
$log\left(y+1\right)+logc=log\left(x-1\right)$
$\Rightarrow \left(y+1\right)c=\left(x-1\right)$
Now, $y\left(1\right)=2$
$\Rightarrow 3c=0$
$\Rightarrow c=0$
$\therefore x-1=0$
$\Rightarrow x=1$
Hence, only one solution exists.