u=Manipulate[

Plot3D[f[x,t,x0,c,d],{x,minX,maxX},{t,.01,simTime},PlotRange->{Automatic,{0,maxTime},{0,maxF}},
AxesLabel->{"x","t","f(x,t)"},
PlotLabel->Style["Solution to \!\(\*FractionBox[\(\(∂f\)\(\\ \)\), \(∂t\)]\) = c\!\(\*FractionBox[\(\(∂\((x\\ f)\)\)\(\\ \)\), \(∂x\)]\)+ D(((∂^2)f)/(∂(x^2))) \nOrnstein-Ehrenfest process",Small],ImagePadding->55,ImageSize->500,PlotPoints->ControlActive[{30,Round[simTime/10]+5},{30,Round[simTime/10]+5}],Mesh->ControlActive[10,10],MaxRecursion->1]

,
{{c,.001,"c="},0.001,.5,.01,AppearanceElements->All,ContinuousAction->False},
{{d,.5,"D="},.1,5,.01,AppearanceElements->All,ContinuousAction->True},
{{simTime,.2,"simulation time="},.1,maxTime,.1,AppearanceElements->All,SynchronousUpdating->True},
Delimiter,
{{x0,0,"x0="},-10,10,.1,AppearanceElements->All,ContinuousAction->True},
{{maxF,.1,"max F="},.01,3,.01,AppearanceElements->All,ContinuousAction->True},
AutorunSequencing->{{3,80}},
Initialization:>
{
minX=-30; maxX=30; maxTime=500;

f[x_,t_,x0_,c_,Diffusion_]:=Module[{μ,σ},
μ=x0 Exp[-c t];
σ=(Sqrt[(Diffusion/c)(1-Exp[-2 c t])]);
(1/(σ(Sqrt[2π])))Exp[-(1/2)(((x-μ)/σ))^2]
]
}
]