∵dx/dt=5x+4y,dy/dt=4x+5y ∴dy/dx=(4x+5y)/(5x+4y)令z=y/x,则dy/dx=z+xdz/dx∴z+xdz/dx=(4+5z)/(5+4z)==>(5+4z)dz/(1-z²)=4dx/x==>[9/(1-z)+1/(1+z)]dz=8dx/x==>ln|1+z|-9ln|1-z|=8ln|x|+ln|C| (C是积分常数)...