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differential-equationsmaximacomputer-algebra-systems
IInatas
IInatas

Reputation: 47

Maxima doesn't find a solution for diff eq with desolve

During my exercise with wxmaxima 11.08.0 (ubuntu 12.04, Maxima version: 5.24.0)
I followed an example from P.Lutus and his second example didn't work for me.

eq: y(t) = -r*c*'diff(y(t),t)+m*sin(%omega*t);
sol:desolve( eq, y(t) );
Is  %omega  zero or nonzero? nonzero

then Maxima isn't reacting anymore until I restart it.
Is there something changed in maxima that I need to activate or define first to get the result ?

The expected output should be:
Intermediate result

There is a second part of my question in case I define the equation by hand:

sol: y(t) = (m * sin(%omega*t))              / (%omega^2*c^2*r^2 + 1) - 
            (%omega*c*m*r*cos(%omega*t))     / (%omega^2*c^2*r^2 + 1) +
            (%omega*c*m*r*%e^-((1*t)/(c*r))) / (%omega^2*c^2*r^2 + 1);

Initial conditions for a continuous process:

init_val:-(c*m*r*(%e^-(t/r*c))*%omega)/(c^2*r^2*%omega^2+1); 
atvalue(y(t),t=0, init_val);
try2 : desolve(sol,y(t));
"Is  "%omega"  zero or nonzero?" nonzero;

last term still there

Here the last term is still there. Are these problems based on the use of trigonometric functions ?

Best regards, Marcus


I updated via PPA to wxMaxima 13.04.0 & Maxima 5.29.1. Now desolve fnished, but the last term seems very complicated. maxima 5.29.1 desolve result

Doing the init_val with the negativ last term and desolve command still leaves the %e^(..)*... in the equation.

Upvotes: 0

Views: 433

Answers (1)

Robert Dodier
Robert Dodier

Reputation: 17576

You might get more interest in this question on the Maxima mailing list. See: http://maxima.sourceforge.net/maximalist.html

For the first version of Lutus example 2, I get:

y(t) = m*sin(%omega*t)/(%omega^2*c^2*r^2+1)
 -%omega*c*m*r*cos(%omega*t)/(%omega^2*c^2*r^2+1)
 +(y(0)*%omega^2*c^3*r^3+%omega*c^2*m*r^2+y(0)*c*r)*%e^-(t/(c*r))
  /(c*r*(%omega^2*c^2*r^2+1))$

which is the same as the expected result, if y(0) = 0. However, I don't see where that is assumed.

After atvalue(y(t),t=0,init_val), I get the same result as Lutus, namely:

y(t) = m*sin(%omega*t)/(%omega^2*c^2*r^2+1)
 -%omega*c*m*r*cos(%omega*t)/(%omega^2*c^2*r^2+1)$

I am working with Maxima 5.31.1, built with Clisp, on Linux.

Upvotes: 1

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