find all equilibrium points of the following systems of diff

find all equilibrium points of the following systems of differential equation and determine their stability properties

a) y\'\'+y\'+3y=0

Solution

y\"+2y\'-3y=0

(e^rx)\"+2(e^rx)^\'-3(e^rx)=0

e^rx(r²+2r-3)=0

r²+2r-3=0

r=1,r=3

y(x)=C₁e^x+C₂e^-3x