Question

dy/ey的积分

Answer 1

∫y/e^y dy
= ∫ye^(-y) dy
= -∫y d[e^(-y)]
= -ye^(-y) + ∫e^(-y) dy,分部积分法
= -ye^(-y) - e^(-y) + C
= -(y+1)e^(-y) + C
例子;
dy/dx=ex/ey求y的通解
这是变量分离方程
变量分离,得:
e^x dx=e^y dy
两边积分,得:
e^x=e^y+C
即y=x+C