Re: Simple ODE with time-dep BC

*To*: mathgroup at smc.vnet.net*Subject*: [mg78022] Re: [mg77933] Simple ODE with time-dep BC*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Thu, 21 Jun 2007 05:52:17 -0400 (EDT)*References*: <24202381.1182335834009.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

The error message is perfectly clear: > DSolve::dvnoarg : The function h appears with no arguments. More... As for the second problem: Once you've said u[t]=v^2, it makes no sense to solve for u[t] -- it's already known (and it doesn't solve the differential equation). But you can use a DIFFERENT t, say t0: DSolve[{u'[t]/2 == -a*u[t] + c, u[t0] == v^2}, u[t], t] {{u[t] -> (\[ExponentialE]^(-2 a t) (c \[ExponentialE]^(2 a t) - c \[ExponentialE]^(2 a t0) + a \[ExponentialE]^(2 a t0) v^2))/ a}} Bobby On Wed, 20 Jun 2007 04:27:35 -0500, Apostolos E. A. S. Evangelopoulos <a.e.a.evangelopoulos at sms.ed.ac.uk> wrote: > Hello all, > > I'm having 2 problems with solving the following ordinary differential > equation: > > h*h'[t]==-a*h^2+c > > Problem 1: > Mathematica doesn't like the form of the above: > DSolve[{h'[t]\[Equal]-a*h[t]+c/h, h[0]\[Equal]0}, h[t], t] > returns > DSolve::dvnoarg : The function h appears with no arguments. More... > > If, now, I reduce the above equation to > DSolve[{1/2*u'[t]\[Equal]-a*u[t]+c,u[0]\[Equal]0},u[t],t] > (by substitution of u=h^2) > then Mathematica solves for u[t] without complaints. The thing is, > though, I could solve the latter by hand, really, so what's the point? > Is Mathematica not supposed to be able to solve the equation in the > first form, really (it appears to be non-linear, but intrinsically it' s > not)? > > Problem 2: > I 'd like to impose a time dependent boundary condition, so, instead of > h[0]u=0, something like h[t]==v (some constant), or, the more > complicated, h[t]==t. How do I solve that? I have tried as follows , with > the reduced u[t] form: > DSolve[{u'[t]/2\[Equal]-a*u[t]+c,u[t]\[Equal]v^2},u[t],t] > resulting in > DSolve::overdet : The system has fewer dependent variables than > equations, so is overdetermined. More... > > Thank you, all, for your help, in advance. > > Apostolos > > -- DrMajorBob at bigfoot.com