how will maple response to non-unique solutions??

Posted on 2008-02-24 12:16 By casperyc ( Maple Rating 2

145)

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How do I ...? with Maple (Student)

dsolve( {diff(x(t),t)=sqrt(x(t)), x(0)=0}, x(t));

use the theorem to test the ODE ,the solutions are unique

however maple gives me a unique solution?

use the theorem to test the

Comment on 2008-02-24 12:16 from casperyc ( Maple Rating 2

145)

use the theorem to test the ODE ,the solutions are NOT unique

however maple gives me a unique solution?

dsolve and non-unique solutions

Comment on 2008-02-24 18:04 from Robert Israel ( Maple Rating 4

1555)

Basically, dsolve is set up for the "usual" situation where you have existence and uniqueness. If you want to deal with one of these pathological situations, you must do some careful analysis. Start with the general solution

> dsolve(diff(x(t),t) = sqrt(x(t)));

x(t)^(1/2)-1/2*t-_C1 = 0

Note that this does not include the singular solution x(t) = 0. Maple's solution is defined for t >= - 2 _C1, but can be continued as x(t) = 0 for t < -2 _C1. In particular this gives solutions satisfying x(0)=0 for any _C1 <= 0.