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I'm struggling to find a way to switch from a symbolic declaration of the differential operator to its implementation

I give you an example.

F: (10-'diff(x(t),t)^2 -2*x(t)*'diff(x(t),t) -5*x(t)^2)*%e^(-t);

E: ratsimp(diff(F, x(t)) - diff(diff(F, 'diff(x(t),t)), t));

sol: ode2(E, x(t), t);
sol: ev(sol, [%k1 = C1, %k2=C2]);

trans_cond: diff(F, 'diff(x(t), t));
trans_cond: ev(trans_cond, sol);
trans_cond: at(trans_cond, [t=1]);

The corresponding output maintains the symbolic notation whereas I would like to evaluate the diff() obtained after the last substitution.

Giving the result:

% 4*C1-C2^(-2)
Marco Repetto
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2 Answers2

3

Another solution. The nouns option for ev causes the evaluation of symbolic derivatives, and also any other noun expressions such as symbolic integrals, symbolic summations, etc.

(%i2) 'diff(4*x^2, x);
                            d      2
(%o2)                       -- (4 x )
                            dx
(%i3) ev (%o2, nouns);
(%o3)                          8 x

A shorter form of ev(..., nouns) is recognized by the interactive console. You can input ..., nouns instead.

(%i5) %o2, nouns;
(%o5)                          8 x

Here is ev(..., nouns) applied to symbolic integral:

(%i6) 'integrate (x^2, x);
                             /
                             [  2
(%o6)                        I x  dx
                             ]
                             /
(%i7) %, nouns;
                                3
                               x
(%o7)                          --
                               3

and here, to a symbolic summation:

(%i8) 'sum (f(k), k, 1, 3);
                            3
                           ====
                           \
(%o8)                       >    f(k)
                           /
                           ====
                           k = 1
(%i9) %, nouns;
(%o9)                  f(3) + f(2) + f(1)
Robert Dodier
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0

Found the answer, ev() carries the option diff which solves all the symbolic differentiation in the expression.

Marco Repetto
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