Merge pull request #768 from KPCCoiL/fix-C14-example

Correct physics of C14 example

Author: ChrisRackauckas

docs/src/examples/classical_physics.md

@@ -15,24 +15,24 @@ using OrdinaryDiffEq, Plots
 gr()
 
 #Half-life of Carbon-14 is 5,730 years.
-C₁ = 5.730
+t½ = 5.730
 
 #Setup
 u₀ = 1.0
-tspan = (0.0, 1.0)
+tspan = (0.0, 30.0)
 
 #Define the problem
-radioactivedecay(u, p, t) = -C₁ * u
+radioactivedecay(u, p, t) = -log(2) / t½ * u
 
 #Pass to solver
 prob = ODEProblem(radioactivedecay, u₀, tspan)
 sol = solve(prob, Tsit5())
 
 #Plot
 plot(sol, linewidth = 2, title = "Carbon-14 half-life",
-    xaxis = "Time in thousands of years", yaxis = "Percentage left",
+    xaxis = "Time in thousands of years", yaxis = "Ratio left",
     label = "Numerical Solution")
-plot!(sol.t, t -> exp(-C₁ * t), lw = 3, ls = :dash, label = "Analytical Solution")
+plot!(sol.t, t -> 2^(-t / t½), lw = 3, ls = :dash, label = "Analytical Solution")
 ```
 
 ## Second Order Linear ODE