Section 5.5 HW 

For all the following problems: 

a) Find the fundamental matrix for the system,   

b) Use the matrix exponential,  

to find the solution,

Where:   for problems 1,

and       for problems 9, 13, 15

Find the general solutions for the following systems: 

                      Answer:  x₁(t) = c₁e^-t + c₂e^3t, x₂(t) = -c₁e^-t + c₂e^3t 

 

         Answer:  x₁(t) = c₁e^5t + 7c₂e^5t+ 3c₃e^9t, x₂(t) = 2c₁e^5t, x₃(t) = 2c₂e^5t+ c₃e^9t

      
Answer:  x₁(t) = (c₁ + c₂t+ (1/2)c₃t²)e^-t, x₂(t) = (2c₂ + c₃ + 2c₃t)e^-t, x₃(t) = (c₂+ c₃t)e^-t

Answer:  x₁(t) = (3c₁ + c₃ - 3c₃t)e^t, x₂(t) = (-c₁ + c₃t)e^t, x₃(t) = (c₂+ c₃t)e^t