求微分方程通解 d^2y／dx^2-e^y* dy／dx=0
问题描述：
求微分方程通解 d^2y／dx^2-e^y* dy／dx=0
答
令p=dy/dx, 则d^2y/dx^2=pdp/dy
代入方程：pdp/dy-e^yp=0
dp/dy=e^y
dp=e^ydy
积分：p=e^y+c
dy/dx=e^y+c
dy/(e^y+c)=dx
d(e^y)/[e^y(e^y+c)]=dx
d(e^y)[1/e^y-1/(e^y+c)]=cdx
积分：lne^y/(e^y+c)=cx+c1
e^y/(e^y+c)=c1e^(cx)
解得：
y=ln{cc1e^(cx)/[1-c1e^(cx)]}