Solution to a Homogeneous Differential Equation

Question

Which of the following is a solution to the differential equation $$\frac{dy}{dx} = \frac{y}{x} + \frac{x}{y}$$ for $$x > 0$$ and $$y > 0$$?

Accepted Answer

$$y = x\sqrt{2 \ln x + C}$$, where $$C$$ is a constant

Answer

$$y = x e^{C}$$, where $$C$$ is a constant

Answer

$$y = x^2 + C$$, where $$C$$ is a constant

Answer

$$y = \sqrt{x^3 + C}$$, where $$C$$ is a positive constant

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