问题描述: (y^2-2xy)dx+x^2dy=0 齐次微分方程!麻烦大虾们帮个忙啊 1个回答 分类:数学 2014-10-16 问题解答: 我来补答 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) = lnxln(v/(1-v))=lnx+lncv/(1-v)=cx(y/x)/(1-(y/x))=cxy/(x-y)=cxy=cx(x-y) 展开全文阅读