(Solved): 37) a) Write the initial value problem in vector form. b) Solve by using eigenvalues/eigenvectors. c ...

Expert Answer

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a) To write the initial value problems in vector form, we introduce a vector function:

  

For problem 36, the system of differential equations can be written in vector form as:

  
with the initial condition:

  

Similarly, for problem 37, the system of differential equations can be written in vector form as:

  
with the initial condition:

  

b) To solve these systems using eigenvalues and
eigenvectors, we first find the eigenvalues and