dy/dx=1+1/(x-y)

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/17 20:46:11

dy/dx=1+1/(x-y)

dy/dx-1=1/(x-y)
(dy-dx)/dx=1/(x-y)
d(y-x)/dx=-1/(y-x)
令 u=y-x
du/dx=-1/u 现在可以分离变量了
udu=-dx
两边积分得 (1/2)u^2=-x+C
原方程的解为 (1/.2)(y-x)^2=-x+C
或者写成 (y-x)^2=-2x+C

dy/dx = 1/x-y dy/dx=x(1-y) 求解dy/dx=(x+y)/(x+y+1) dy/dx,y=(1+x+x^2)e^x 设y=（x/1-x)^x,求dy/dx 解, Dy/Dx + y = x , y(0) = 1 dy/dx=x(1+y^2)/y通解 cos(x+y)+y=1 求dy/dx dy/dx-2y/(1+x)=(x+1)^3 dy/dx-2y/(x+1)=(x+1)^2 dy/dx=(e^x+x)(1+y^2)通解从(dx)/(dy)=1/y '导出：(d^2x)/(dy^2)=-y''/(y')^3