dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急

问题描述:

dy/dx=(2y+4)/(x+y-1 ) 解这个方程 十万火急
如题

dy/dx=(2y+4)/(x+y-1 )设Y= y+2 X=x-3 代入:dY/dX=2Y/(X+Y)2dX/dY=X/Y+1设U=X/Y X=YU dX/dY=U+YdU/dY 代入:2(U+YdU/dY)=U+12dU/(1-U)=dY/Y积分得:-2ln(1-U)+lnC=lnYY(1-U)²=CY(1-X/Y)²=C(Y-X)²=CY...