(x-2y)dy+dx=0的通解

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/15 16:29:05

(x-2y)dy+dx=0的通解
求求怎么写啊

∵(x-2y)dy+dx=0
==>xe^ydy-2ye^ydy+e^ydx=0 (等式两端同乘e^y)
==>xd(e^y)+e^ydx=2yd(e^y)
==>d(xe^y)=2yd(e^y)
==>∫d(xe^y)=∫2yd(e^y)
==>xe^y=2(y-1)e^y+C (C是常数)
==>x=2(y-1)+Ce^(-y)
∴原方程的通解是x=2(y-1)+Ce^(-y).
再问：哇噻这个才是正确的

dy/dx-2+y/x=0的通解是什么? (x-2y)dy+dx=0的通解求dx+(x+y^2)dy=0的通解微分方程(x+y)(dx-dy)=dx+dy的通解 dy/dx=-y/x 的通解微分方程dy/dx=y/(x+y^2)的通解? dy/ dx +2y=x*e^x的通解, (x+x^2y)dx -(x^2y+y)dy =0的通解 dy/dx=1/(x+y)^2的通解为求dy/dx=(x+y)^2的通解 dy/dx=-y^2/x的通解求dy/dx=2x+y的通解.