> dsolve({diff(y(t), t) = t^9/y(t)^3, y(1) = 9}, y(t));
                                              (1/4)

                    1  (1/2) /    10         \     

             y(t) = - 5      \10 t   + 164015/     

                    5                              


;
> dsolve({(D@@2)(y)(t) + 20*D(y)(t) + 62*y(t) = 0, y(0) = 1, D(y)(0) = 0}, y(t));
                /1   5    (1/2)\    //        (1/2)\  \

         y(t) = |- + -- 38     | exp\\-10 + 38     / t/

                \2   38        /                       



              /1   5    (1/2)\    / /       (1/2)\  \

            + |- - -- 38     | exp\-\10 + 38     / t/

              \2   38        /                       




;
> a1 := 55;
> a2 := 62;
> a3 := 22;
> A := Matrix([[a1, a2, a3], [a2, a3, a1], [a3, a2, a1]]);
                            [55  62  22]

                            [          ]

                       A := [62  22  55]

                            [          ]

                            [22  62  55]


;
> with(LinearAlgebra);
> evalf(Eigenvalues(A));
                         [&uminus0;40.]

                         [            ]

                         [    33.     ]

                         [            ]

                         [    139.    ]


;
> evalf(Eigenvectors(A));
[    33.     ]  [&uminus0;0.8937836515            1.           1.]

[            ]  [                                                ]

[&uminus0;40.], [&uminus0;0.03768967205  &uminus0;1.887096774  1.]

[            ]  [                                                ]

[    139.    ]  [          1.                     1.           1.]


;
# all values =0 are replaced with 1