#OK to post homework

#Nicholas DiMarzio, 11/1/21, Assignment 16

#
#Problem 1
dsolve({diff(x(t), t) = 3*x(t) - y(t), diff(y(t), t) = 2*x(t), x(0) = 2, y(0) = 3}, {x(t), y(t)});
     {x(t) = exp(t) + exp(2 t), y(t) = 2 exp(t) + exp(2 t)}

#Problem 2
dsolve({diff(x(t), t) = x(t) + 8*y(t), diff(y(t), t) = -y(t), x(0) = 1, y(0) = 9}, {x(t), y(t)});
       {x(t) = -36 exp(-t) + 37 exp(t), y(t) = 9 exp(-t)}

#Problem 3
M := Matrix([[1, 1, 1], [1, 1, 0], [1, 0, 0]]);
                              [1  1  1]
                              [       ]
                         M := [1  1  0]
                              [       ]
                              [1  0  0]

N = evalf(Eigenvalues(M));
     [[                       &uminus0;10             ]  
 N = [[2.246979605 + 1.times10            ⅈ], 

   [                                          &uminus0;10 
   [&uminus0;0.8019377358 - 1.866025404times10            

               ]  
   ⅈ], 

   [                                 &uminus0;11             ]]
   [0.5549581322 - 1.339745960times10            ⅈ]]


F = evalf(Eigenvectors(M));
    /[[                       &uminus0;10             ]  
F = \[[2.246979605 + 1.times10            ⅈ], 

  [                                          &uminus0;10 
  [&uminus0;0.8019377358 - 1.866025404times10            

              ]  
  ⅈ], 

  [                                 &uminus0;11             ]]  
  [0.5549581322 - 1.339745960times10            ⅈ]], 

  [[                                &uminus0;9               
  [[2.246979634 + 1.514675242times10           ⅈ, 

                                            &uminus0;10 
  &uminus0;0.8019377350 + 3.686305552times10            

  ⅈ, 

                                   &uminus0;11             ]  
  0.5549581323 - 2.254559307times10            ⅈ], 

  [                                &uminus0;9               
  [1.801937769 + 1.888769131times10           ⅈ, 

                                   &uminus0;10               
  0.4450418682 - 5.947994638times10            ⅈ, 

                                           &uminus0;11 
  &uminus0;1.246979604 + 5.809451696times10            

              ]              ]\
  ⅈ], [1., 1., 1.]]/


dsolve({diff(x1(t), t) = x1(t) + x2(t) + x3(t), diff(x2(t), t) = x1(t) + x2(t), diff(x3(t), t) = x1(t), x1(0) = 1, x2(0) = 2, x3(0) = -1}, {x1(t), x2(t), x3(t)});

#Problem 4