describe SciMax Toolbox determinant

SciMax Toolbox >> desolve

desolve

Maxima Function

Calling Sequence

desolve (eqn, x)
desolve([eqn_1,...,eqn_n],[x_1,...,x_n])

Description

The function dsolve solves systems of linear ordinary differential equations using Laplace transform. Here the eqn's are differential equations in the dependent variables x_1, ..., x_n. The functional dependence of x_1, ..., x_n on an independent variable, for instance x, must be explicitly indicated in the variables and its derivatives. For example, this would not be the correct way to define two equations:

eqn_1: 'diff(f,x,2) = sin(x) + 'diff(g,x);
eqn_2: 'diff(f,x) + x^2 - f = 2*'diff(g,x,2);

The correct way would be:

eqn_1: 'diff(f(x),x,2) = sin(x) + 'diff(g(x),x);
eqn_2: 'diff(f(x),x) + x^2 - f(x) = 2*'diff(g(x),x,2);

The call to the function desolve would then be

desolve([eqn_1, eqn_2], [f(x),g(x)]);

If initial conditions at x=0 are known, they can be supplied before calling desolve by using atvalue.

(%i1) <b><code class="literal">'diff(f(x),x)='diff(g(x),x)+sin(x);</code></b>
                 d           d
(%o1)            -- (f(x)) = -- (g(x)) + sin(x)
                 dx          dx
(%i2) <b><code class="literal">'diff(g(x),x,2)='diff(f(x),x)-cos(x);</code></b>
                  2
                 d            d
(%o2)            --- (g(x)) = -- (f(x)) - cos(x)
                   2          dx
                 dx
(%i3) <b><code class="literal">atvalue('diff(g(x),x),x=0,a);</code></b>
(%o3)                           a
(%i4) <b><code class="literal">atvalue(f(x),x=0,1);</code></b>
(%o4)                           1
(%i5) <b><code class="literal">desolve([%o1,%o2],[f(x),g(x)]);</code></b>
                  x
(%o5) [f(x) = a %e  - a + 1, g(x) =
                                                x
                                   cos(x) + a %e  - a + g(0) - 1]
(%i6) <b><code class="literal">[%o1,%o2],%o5,diff;</code></b>
             x       x      x                x
(%o6)   [a %e  = a %e , a %e  - cos(x) = a %e  - cos(x)]

If desolve cannot obtain a solution, it returns false.

describe SciMax Toolbox determinant