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AP Calculus AB/Unit 7: Differential Equations
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Particular Solution to a Differential Equation

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What is the particular solution to the differential equation dydx=4y2x3 \frac{dy}{dx} = \frac{4y}{2x - 3} with the initial condition y(2)=12 y(2) = \frac{1}{2} for x>32 x > \frac{3}{2} ?

A

y=12(2x3)2 y = \frac{1}{2}(2x - 3)^2

B

y=12e4x6 y = \frac{1}{2}e^{4x - 6}

C

y=12ln(2x3)+12 y = \frac{1}{2}\ln(2x - 3) + \frac{1}{2}

D

y=2x2 y = 2x - 2

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