(y^2-2xy)dx+x^2dy=0 齐次微分方程!

题目

(y^2-2xy)dx+x^2dy=0 齐次微分方程!
麻烦大虾们帮个忙啊

答案

令：v=y/x,y=xv,dy=vdx+xdvdy/dx = -(y^2-2xy)/x^2(vdx+xdv)/dx = 2v - v^2v+xdv/dx = 2v - v^2xdv/dx = v - v^2dv/[v(1 - v)] = dx/x∫dv/[v(1 - v)] = ∫dx/x∫dv/v + ∫dv/(1 - v)] = ∫dx/xlnv - ln(1-v) = lnxl...