Lambert function and solution y=x*exp(dx/dt*t) for x

[dkazmer]

Hi,

 

I've been working through some derivations for constitutive models of viscoelasticity, and they've been leading me to forms involving the Lambert (product log) function. The solutions get complex very quickly.

 

In an attempt to simplify, I'm trying the simplest possible constitutive model having the form y=x*exp(dx/dt*t).

 

Now this is where things get strange: Mathematica (Wolfram Alpha) returns a solution of y=x for Solve[y==x*E^[D[x,t]*t],x].

 

Any thoughts?

 

Best wishes! David Kazmer

 

 

Just following up a bit, an equivalent form is Solve[log(y/x)=t*dx/dt,x]

 

which is recognized as a non-linear ODE and yields y Ei(-log(y/(x(t))))+log(t) = 0

 

I guess I'm surprised that the initial problem wasn't recognized as a NL-ODE by Mathematica, and that isn't readily solvable...