Discussion
The solution of the differential equation \((2y - 1)dy - (y - 2)dx = 0\) is
Answer: D
The solution is \(2y + 3\log|y - 2| = x + c\).
Separate the variables and split the fraction:
\[ \begin{aligned} \frac{2y - 1}{y - 2}\,dy &= dx \\ \left(2 + \frac{3}{y - 2}\right)dy &= dx \\ 2y + 3\log|y - 2| &= x + c \end{aligned} \]
(\(2y - 1 = 2(y - 2) + 3\).) The other options have the wrong coefficient on \(y\), on the logarithm or on \(x\).
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