APFIVE Particular Solution to a Differential Equation
Which of the following is the particular solution to the differential equation $$\displaystyle\frac{dy}{dx} = 3y^2$$ with the initial condition $$y(0) = \displaystyle\frac{1}{2}$$?
A
$$\displaystyle y = \frac{3x}{2} + \frac{1}{2}$$
B
$$\displaystyle y = \frac{1}{2 + 3x}$$
C
$$\displaystyle y = \frac{1}{2}e^{3x}$$
D
$$\displaystyle y = \frac{1}{2 - 3x}$$
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