APFIVE Particular Solution to a Differential Equation
What is the particular solution to the differential equation $$ \frac{dy}{dx} = \frac{4y}{2x - 3} $$ with the initial condition $$ y(2) = \frac{1}{2} $$ for $$ x > \frac{3}{2} $$?
A
$$ y = \frac{1}{2}e^{4x - 6} $$
B
$$ y = \frac{1}{2}\ln(2x - 3) + \frac{1}{2} $$
C
$$ y = 2x - 2 $$
D
$$ y = \frac{1}{2}(2x - 3)^2 $$
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