Solving a Separable Differential Equation

Question

Which of the following is the solution to the differential equation $$\displaystyle\frac{dy}{dx} = 2y^2$$ with the initial condition $$y(0) = \displaystyle\frac{1}{3}$$?

Accepted Answer

$$\displaystyle y = \frac{1}{3 - 2x}$$

Answer

$$\displaystyle y = \frac{1}{3}e^{2x}$$

Answer

$$\displaystyle y = \frac{1}{3 + 2x}$$

Answer

$$\displaystyle y = \sqrt{\frac{1}{9} + 2x}$$

Solving a Separable Differential Equation

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