dy/dx = ((x^2)+(3y^2))/(2xy)
dy/dt = (1+3y^2/x^2)/(2y/x)
let u = y/x, then y = ux
dy/dx = d(ux)/dx = (du/dx)*x + u = (1+3u^2) / (2u) = 1/(2u) + 3u/2
(du/dx)*x= 1/(2u) + u/2 = (1+u^2)/(2u)
∫ ( (2u) / (1+u^2) ) du = ∫ (1/x) dx
ln|1+(y/x)^2| = ln|x| + c
1+u = ax, a = e^c
1 + (y^2)/(x^2) - ax = 0
y^2 + x^2 - ax^3 = 0
