calculus,y''+4y'+3y=0,y(0)=0,y'(0)=1,y=?
问题描述：
calculus,y''+4y'+3y=0,y(0)=0,y'(0)=1,y=?
答
characteristic equationr^2+4r+3=0(r+1)(r+3)=0r=-1,-3y=Ae^(-t)+Be^(-3t)Plug in t=0,y=0A+B=0 (1)y'=-Ae^(-t)-3Be^(-3t)Plug in t=0,y'=1-A-3B=1 (2)(1)+(2):-2B=1B=-1/2A=-B=1/2y=(1/2)e^(-t)-(1/2)e^(-3t)