Discussion
The general solution of the differential equation \((1 + y)dx - (1 - x)dy = 0\) is
Answer: C
The solution is \(x - y + xy = C\).
Separate the variables:
\[ \begin{aligned} \frac{dx}{1 - x} &= \frac{dy}{1 + y} \\ -\log|1 - x| &= \log|1 + y| + c \\ (1 - x)(1 + y) &= k \end{aligned} \]
Expanding, \(1 + y - x - xy = k\), that is \(x - y + xy = C\). Check: differentiating \(x - y + xy = C\) gives \((1 + y)dx + (x - 1)dy = 0\), the given equation. The other options give different equations on differentiation.
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