求解常微分方程y'=(2*x-y-1)/(x-2*y+1)的通解,要求过程尽量详细,写出每一步?
问题描述：
求解常微分方程y'=(2*x-y-1)/(x-2*y+1)的通解,要求过程尽量详细,写出每一步?
答
此题最简单的解法：全微分法.∵y'=(2x-y-1)/(x-2y+1) ==>(x-2y+1)dy-(2x-y-1)dx=0==>(xdy+ydx)-2xdx-2ydy+dy+dx=0==>d(xy)-d(x²)-d(y²)+dx+dy=0==>d(xy-x²-y²+x+y)=0==>xy-x²-y²+x+y=...