求y+dy/dx=e的负x次幂
问题描述:
求y+dy/dx=e的负x次幂
答
y' + y = e^(-x)
积分因子= e^∫ dx = e^x
e^x • y' + e^x • y = e^x • e^(-x)
(ye^x)' = 1
ye^x = x + C
y = xe^(-x) + Ce^(-x)