using DifferentialEquations, Plots;

f(y,p,t)=p*y;

deqprbl=ODEProblem(f,3.0,(0.0,12.0),-0.33)

ODEProblem with uType Float64 and tType Float64. In-place: false
Non-trivial mass matrix: false
timespan: (0.0, 12.0)
u0: 3.0

solu=solve(deqprbl)

retcode: Success
Interpolation: 3rd order Hermite
t: 11-element Vector{Float64}:
  0.0
  0.12483206655122647
  0.6886030741856269
  1.5683314195545082
  2.5697752584258504
  3.814990854882284
  5.211084672862995
  6.787294336984937
  8.495975157356488
 10.33295133653541
 12.0
u: 11-element Vector{Float64}:
 3.0
 2.878927148046797
 2.390190997811257
 1.7879380049976432
 1.2847790129192596
 0.8518596122098523
 0.5373839046768774
 0.3194396051680836
 0.1817645018746746
 0.09913909588840228
 0.05719147224311148

plot(t->solu(t),0,12,legend=false,title="Lösung des AWP")

scatter!(solu.t,solu.u,xlabel="Zeit t",ylabel="Menge y(t)")

function f!(yp,y,p,t) 
    g=p[1]; l=p[2];
   yp[1]=y[2];
   yp[2]=-g*sin(y[1])/l;
   return;
end;
y0=[0.0,6.26]; tspan=(0.0,12.0); p=(9.81,1.0);    
pendprob=ODEProblem(f!,y0,tspan,p)

ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 12.0)
u0: 2-element Vector{Float64}:
 0.0
 6.26

pendsol=solve(pendprob,reltol=1.0e-4)

retcode: Success
Interpolation: 3rd order Hermite
t: 77-element Vector{Float64}:
  0.0
  0.0015948963317384368
  0.013261602775004096
  0.039563636350133734
  0.07848460760072484
  0.12885739197020463
  0.19378324959991539
  0.27140427112112103
  0.3656724096299395
  0.48660050305089914
  0.6133868267665499
  0.7455284551837222
  0.8857316437369804
  ⋮
 10.089214893133336
 10.262092120572163
 10.437589645376253
 10.605917510186504
 10.759790038210822
 10.938660108296784
 11.119812229409316
 11.30889283554939
 11.496590610764633
 11.679028259801468
 11.855367568005446
 12.0
u: 77-element Vector{Vector{Float64}}:
 [0.0, 6.26]
 [0.009984009513870205, 6.259921895914342]
 [0.08299377212857774, 6.254603730701196]
 [0.24703694195328355, 6.212242841521462]
 [0.4864388506606143, 6.075503550012873]
 [0.7855992239020742, 5.782581208969148]
 [1.1447980337661436, 5.260719868236802]
 [1.5249775777062335, 4.523963760043152]
 [1.908212614037087, 3.6155766546696206]
 [2.281822321400845, 2.600647274515747]
 [2.5573939436173387, 1.7892730215689738]
 [2.7518637404071216, 1.1911623804865483]
 [2.886759129333568, 0.7623826770073654]
 ⋮
 [-2.9904964516139154, -0.41690103299178743]
 [-3.043503705216938, -0.21113916763746918]
 [-3.067274804300176, -0.06652721531394024]
 [-3.0684379397922297, 0.05238769543703016]
 [-3.0514088524981724, 0.1732058901599721]
 [-3.0042845460704464, 0.36732916643025837]
 [-2.9115387784321967, 0.6835012302989832]
 [-2.7337762346979493, 1.2487272762977224]
 [-2.416951293256817, 2.2090788423968113]
 [-1.8891317324576662, 3.6646369049045977]
 [-1.093326536600427, 5.346665880770893]
 [-0.2462563390906526, 6.212793835761673]

plot(t->pendsol(t)[1],0,12,label="Winkel",
   xlabel="Zeit t")
plot!(t->pendsol(t)[2],0,12,label="Spin",
   ylabel="Winkel und Spin")

phpl=plot(t->pendsol(t)[1],t->pendsol(t)[2],0,12,leg=false,
    title="Phasenportrit",xlabel="Winkel",ylabel="Spin")

Differentialgleichungen¶

Erstes Beispiel¶

Exponentieller Zerfall¶

Zweites Beispiel¶

System von 2 ODEs (Pendel)¶