Differential Equations
Homogeneous Differential Equations
Premium Question
Grade 12
Question:
The general solution of $(x^2 + y^2)dx = 2xy \, dy$ is:
(1) $x^2 + y^2 = Cx$
(2) $x^2 - y^2 = Cx$
(3) $y^2 - x^2 = Cx$
(4) $x^2 - y^2 = Cy$
Step-by-Step Solution
Key Concept: Rewrite as $\frac{dy}{dx} = \frac{x^2 + y^2}{2xy}$, substitute $y = vx$ to make it separable, and simplify $\frac{1 + v^2}{2v} - v$ before integrating.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)