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