given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0
问题描述：
given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0
答
这句话的意思是已知y=(1+4x)e^(-2x) 证明d^2 y/dx^2+2dy/dx+xy=0
证明:
dy/dx=4e^(-2x)-2(1+4x)e^(-2x)
d^2 y/dx^2=-8e^(-2x)-8e^(-2x)+4(1+4x)e^(-2x)
xy=x(1+4x)e^(-2x)
上三式相加得d^2 y/dx^2+2dy/dx+xy=0