APFIVE Solving a Separable Differential Equation
Which of the following is the solution to the differential equation $$\displaystyle\frac{dy}{dx} = 2y^2$$ that satisfies the initial condition $$y(0) = \displaystyle\frac{1}{3}$$?
A
$$\displaystyle y = \frac{1}{3}e^{2x}$$
B
$$\displaystyle y = \frac{1}{3 - 2x}$$
C
$$\displaystyle y = \sqrt{\frac{1}{9} + 2x}$$
D
$$\displaystyle y = \frac{1}{3 + 2x}$$
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