Explanation

(a)
Given equation is $\frac{dy}{dx} = \frac{y + 1}{x - 1}\ \Rightarrow \ \frac{dy}{y + 1} = \frac{dx}{x - 1}$
On integrating both sides
$\int_{}^{}{\frac{dy}{y + 1} = \int_{}^{}\frac{dx}{x - 1}}$
$\Rightarrow \log{(y + 1) = \log{(x - 1) + \log c}}$
$\Rightarrow \log{(y + 1) = \log{(x - 1)c}}$
$\Rightarrow y + 1 = (x - 1)c$
At $x = 1\ \Rightarrow y = - 1$
Whereas $y(1) = 2$.
Hence, the above solution is not possible.