Answer:
1) m=[1,4]
2) m=[-3,0,1]
Step-by-step explanation:
for y= e^(m*x) , then
y′=m*e^(m*x)
y′′=m²*e^(m*x)
y′′′=m³*e^(m*x)
thus
1) y′′+3y′−4y=0
m²*e^(m*x) + 3*m*e^(m*x) - 4*e^(m*x) =0
e^(m*x) *(m²+3*m-4) = 0 → m²+3*m-4 =0
m= [-3±√(9-4*1*(-4)] /2 → m₁=-4 , m₂=1
thus m=[1,4]
2) y′′′+2y′′−3y′=0
m³*e^(m*x) + 2*m²*e^(m*x) - 3*m*e^(m*x) =0
e^(m*x) *(m³+2*m²-3m) = 0 → m³+2*m²-3m=0
m³+2*m²-3m= m*(m²+2*m-3)=0
m=0
or
m= [-2±√(4-4*1*(-3)] /2 → m₁=-3 , m₂=1
thus m=[-3,0,1]
