Final answer:
The general solution of the homogeneous differential equation (2yx² y³)dx = (2xy² x³)dy is y² - xy³ = Cx.
Step-by-step explanation:
The given differential equation is (2yx² y³)dx = (2xy² x³)dy.
To find the general solution, we can separate the variables and integrate both sides. Rearrange the equation to obtain:
(2yx²)dx = (2xy²)dy.
Divide both sides by x²y³:
2dx/x² = 2dy/y³.
Now integrate both sides:
∫2dx/x² = ∫2dy/y³.
After integrating, we get:
-2/x = -2/y² + C,
where C is the constant of integration.
Therefore, the general solution of the homogeneous differential equation is y² - xy³ = Cx.