Solving a Separable Differential Equation

Question

Consider the solution process for the differential equation $$\frac{dy}{dx}= \frac{4x}{y}$$ with the initial condition $$y(0)=5$$. Which of the following options presents a correct sequence of equations that appear during this process?

Accepted Answer

$$\frac{y^2}{2}=2*x^2+\frac{25}{2}, y^2=4*x^2+25, y=\sqrt{4*x^2+25}, y=-\sqrt{4*x^2+25}$$

Answer

$$y=\sqrt{4*x^2+25}, \frac{y^2}{2}=2*x^2+\frac{25}{2}, y^2=4*x^2+25, y=-\sqrt{4*x^2+25}$$

Answer

$$y^2=4*x^2+25, y=\sqrt{4*x^2+25}, \frac{y^2}{2}=2*x^2+\frac{25}{2}, y=-\sqrt{4*x^2+25}$$

Answer

$$y=\sqrt{4*x^2+25}, y^2=4*x^2+25, \frac{y^2}{2}=2*x^2+\frac{25}{2}, y=-\sqrt{4*x^2+25}$$

Solving a Separable Differential Equation

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