I would like to use DSolve (or NDSolve) to verify that the solution to the ODE problem

`-4(v''[t]+(2/r)v'[t])-2*v[t]*Log[v[t]]-(3+(3/2)Log[4 Pi])*v[t]==0, `

with conditions $ \lim_{t\to \infty}v(t)=0$ and $ v'(0)=0$ is given by

`v[t]=(4 Pi)^(-3/4)*Exp[-t^2/8]. `

I am able to verify this by hand, but am having trouble using Mathematica to verify it. I would like to use Mathematica to solve this differential equation, and later on modify some terms in the ODE to see how the solution changes.

Perhaps I am making a foolish mistake. I have also tried using NDSolve, but did not obtain the correct solution. I would appreciate any tips. Below you can find the picture of the error messages. Thanks for your help.

Picture of output

`sol=DSolve[{-4(v''[t]+(2/r)v'[t])-2*v[t]*Log[v[t]] -(3+(3/2)Log[4 Pi])*v[t]==0,v[Infinity]==0,v'[0]==0},v[t],t] Plot[Evaluate[v[t] /. sol], {t, 0, 10}, PlotRange -> All] `