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The Maxima on-line user's manual

Algebra Calculator

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Desolve Calculator

Desolve

Function: desolve (<eqn>, <x>)

eqn:

Function: desolve ([<eqn_1>, ..., <eqn_n>], [<x_1>, ..., <x_n>]) The function desolve 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) diff(f(x),x)=diff(g(x),x)+sin(x);
                           d           d
          (%o1)            -- (f(x)) = -- (g(x)) + sin(x)
                           dx          dx
          (%i2) diff(g(x),x,2)=diff(f(x),x)-cos(x);
                            2
                           d            d
          (%o2)            --- (g(x)) = -- (f(x)) - cos(x)
                             2          dx
                           dx
          (%i3) atvalue(diff(g(x),x),x=0,a);
          (%o3)                           a
          (%i4) atvalue(f(x),x=0,1);
          (%o4)                           1
          (%i5) desolve([%o1,%o2],[f(x),g(x)]);
                            x
          (%o5) [f(x) = a %e  - a + 1, g(x) =

x cos(x) + a %e - a + g(0) - 1]

          (%i6) [%o1,%o2],%o5,diff;
                       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.

(%o1)                                true
(%i2) 

Desolve Example

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