问题描述: 求微分方程dy/dx=(4x+3Y)/(x+y)的通解 1个回答 分类:数学 2014-11-15 问题解答: 我来补答 dy/dx=(4x+3y)/(x+y)dy/dx=3+x/(x+y)y/x=u dy=udx+xduu+xdu/dx=3+1/(1+u)xdu/dx=3-u+1/(1+u)(1+u)du/(4+2u-u^2)=dx/x(-1+u)du/(4+2u-u^2)-2du/(4+2u-u^2)=dx/x(-1/2)dln(4+2u-u^2)-2du/[5-(u-1)^2]=dlnxdu/[√5-(u-1)][√5+(u-1)]=(1/(2√5))[ln(√5+u-1)-ln(√5-u+1)](-1/2)ln(4+2u-u^2)-(1/√5)[ln(√5+u-1)-ln(√5-u+1)]=lnx+C0(-1/2)ln[4+2y/x-(y/x)^2] - (1/√5)[ln(√5+y/x-1) - ln(√5-y/x+1)]=lnx+C0 展开全文阅读