SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/Separation"]

u[x_,t_]:=-2Exp[-16(π^2)t]Sin[4π x]+5Exp[-100(π^2)t]Sin[10π x]

Plot3D[u[x,t],{x,0,1},{t,0,0.01},AxesLabel->{"x","t","u(x,t)"},PlotTheme->"Detailed",PlotRange->All]

Export["heat.pdf",%,"PDF"]

Export["heat.eps",%%,"EPS"]