#OK to post homework
#Nicholas DiMarzio, 09/13/21,Assignment 2
#
#Problem 2
#
dsolve({y(0) = 1, D(y)(t) = y(t)^3/(t + 1)}, y(t));
                                  1           
                 y(t) = ----------------------
                                         (1/2)
                        (1 - 2 ln(t + 1))     


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

#
#Problem 4
#
A := Matrix([[3, -4], [4, 3]]);
                           [3  -4]
                      A := [4   3]

with(LinearAlgebra);
evalf(Eigenvalues)(A);
                      [3 + 4 ⅈ]
                      [                  ]
                      [3 - 4 ⅈ]

evalf(Eigenvectors)(A);
  [3 + 4 ⅈ]  [ⅈ  &uminus0;ⅈ]
  [                  ], [                                   ]
  [3 - 4 ⅈ]  [     1                  1          ]