calculus,y''+4y'+3y=0,y(0)=0,y'(0)=1,y=?

calculus,y''+4y'+3y=0,y(0)=0,y'(0)=1,y=?
calculus,y''+4y'+3y=0,y(0)=0,y'(0)=1,y=?

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