Prove that equation is Homogenous and then solve the following:

Question

Answer 1

f(x, vx) = (x² - k²x²)/(3x²k) = (1 - k²)/(3k);

Let y = vx, then dy/dx = y' = v'x + v; v'x + v = (1 - v²)/(3v); v'x = (1 - 4v²)/(3v)∫;

∫(3v)/(1 - 4v²)dv = ∫dx/x; - 3/8lnI1 - 4v²) = lnIxI + C

-3/8lnI1 - 4y²/x²I = lnIxI + C

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