given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0

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