#### Maxima: ODR s konstantními koeficienty


(%i1) eqn : 'diff(y(x),x,4) + 18 * 'diff(y(x),x,2) + 81 * y(x)=0 ;

4                2
d                d
(%o1)             --- (y(x)) + 18 (--- (y(x))) + 81 y(x) = 0
4                2
dx               dx

(%i2) atvalue(y(x),x=0,0);
(%o2)                                  0

(%i3) atvalue('diff(y(x),x),x=0,9);
(%o3)                                  9

(%i4) atvalue('diff(y(x),x,2),x=0,0);
(%o4)                                  0

(%i5) atvalue('diff(y(x),x,3),x=0,-9);
(%o5)                                 - 9

(%i6) desolve(eqn,y(x));

13 sin(3 x)
(%o6)                  y(x) = ----------- - 4 x cos(3 x)
3

(%i7) tex(%);

$$y\left(x\right)={{13\,\sin \left(3\,x\right)}\over{3}}-4\,x\,\cos \left(3\,x\right)$$


#### Maxima: exponenciála matice


(%i1) A : matrix([1,2],[2,4]);
[ 1  2 ]
(%o1)                              [      ]
[ 2  4 ]

(%i2) matrixexp(A,t);

[    5 t           5 t     ]
[  %e    + 4   2 %e    - 2 ]
[  ---------   ----------- ]
[      5            5      ]
(%o2)                    [                          ]
[     5 t          5 t     ]
[ 2 %e    - 2  4 %e    + 1 ]
[ -----------  ----------- ]
[      5            5      ]

(%i3) B : matrix([2,-1,-1],[2,-1,-2],[-1,1,2]);

[  2   - 1  - 1 ]
[               ]
(%o3)                          [  2   - 1  - 2 ]
[               ]
[ - 1   1    2  ]

(%i4) matrixexp(B,t);

[           t           t             t   ]
[ (t + 1) %e      - t %e        - t %e    ]
[                                         ]
(%o4)             [         t                t           t  ]
[   2 t %e     (1 - 2 t) %e    - 2 t %e   ]
[                                         ]
[         t            t                t ]
[   - t %e         t %e       (t + 1) %e  ]



#### Maxima: (inverzní) Laplaceova transformace


(%i1) laplace(1+sin(t)-cos(t-1),t,p);

cos(1) p + sin(1)     1      1
(%o1)                  - ----------------- + ------ + -
2              2       p
p  + 1         p  + 1

(%i2) ilt((p+1)/(p^2+p+1),p,t);

sqrt(3) t
sin(---------)
- t/2          2            sqrt(3) t
(%o2)              %e      (-------------- + cos(---------))
sqrt(3)               2