化dy/dx=(x+3y-5)/(2x-y+1)为课分离变量方程

题目

化dy/dx=(x+3y-5)/(2x-y+1)为课分离变量方程

答案

解方程x+3y-5=0,2x-y+1=0得x=2/7,y=11/7令u=[y- (11/7)]/[x-(2/7)]则y-(11/7)=[x-(2/7)]u所以dy/dx=d(y-(11/y))/d(x-(2/7)) = [x-(2/7)]u'+u另外(x+3y-5)/(2x-y+1)上下同除x-2/7=(1+3u)/(2-u)所以[x-(2/7)]u'+u=(1+3...