1.构造辅助函数

$$ f+f':F(x)=f(x)e^x\\f'-f=F(x)=f(x)e^{-x}\\ f'+kf:F(x)=f(x)e^{kx}\\ff':F(x)=f^2(x)\\ \frac{f'}{f}:F(x)=lnf\\ff''+f'^2:F(x)=f'(x)f(x)\\ ff''-f'^2:F(x)=\frac{f'(x)}{f(x)}从而F(x)=lnf(x) $$