restart: with(DEtools):with(plots):with(inttrans): sy:=D(y1)(t)=y2(t),D(y2)(t)=-omega^2*y1(t): ## 1. Allgemeine L\366sung dsolve({sy},{y1(t),y2(t)},explicit);
NiM8JC8tSSN5Mkc2IjYjSSJ0R0YnLCQqJkkmb21lZ2FHRiciIiIsJiomSSRfQzFHRidGLS1JJGNvc0c2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YnNiMqJkYsRi1GKUYtRi0hIiIqJkkkX0MyR0YnRi0tSSRzaW5HRjNGNkYtRi1GLUY4Ly1JI3kxR0YnRigsJiomRjBGLUY7Ri1GLSomRjpGLUYxRi1GLQ== ## 2. L\366sung des Anfangswertproblems mit der Option explicit lsg:=dsolve({sy,y1(0)=1,y2(0)=2},{y1(t),y2(t)},explicit); NiM+SSRsc2dHNiI8JC8tSSN5MkdGJTYjSSJ0R0YlLCQqJkkmb21lZ2FHRiUiIiIsJiomRi4hIiItSSRjb3NHNiRJKnByb3RlY3RlZEdGNkkoX3N5c2xpYkdGJTYjKiZGLkYvRitGL0YvISIjLUkkc2luR0Y1RjhGL0YvRjIvLUkjeTFHRiVGKiwmKiZGLkYyRjtGLyIiI0YzRi8= ## 3. L\366sung des Anfangswertproblems mittels Laplace-Transformation dsolve({sy,y1(0)=1,y2(0)=2},{y1(t),y2(t)},method=laplace);
NiM8JC8tSSN5Mkc2IjYjSSJ0R0YnLCYtSSRjb3NHNiRJKnByb3RlY3RlZEdGLkkoX3N5c2xpYkdGJzYjKiZJJm9tZWdhR0YnIiIiRilGMyIiIyomRjJGMy1JJHNpbkdGLUYwRjMhIiIvLUkjeTFHRidGKCwmKiZGMkY4RjZGM0Y0RitGMw== ## 4. Grafische Darstellung der exakten L\366sung (1. M\366glichkeit) z1:=subs(lsg,y1(t)); NiM+SSN6MUc2IiwmKiZJJm9tZWdhR0YlISIiLUkkc2luRzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IyomRigiIiJJInRHRiVGMUYxIiIjLUkkY29zR0YsRi9GMQ== z2:=subs(lsg,y2(t)); NiM+SSN6Mkc2IiwkKiZJJm9tZWdhR0YlIiIiLCYqJkYoISIiLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRiU2IyomRihGKUkidEdGJUYpRikhIiMtSSRzaW5HRi9GMkYpRilGLA== omega:=1: plot({z1,z2},t=0..4*Pi,thickness=4,color=black); 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#y1(t) geht durch den Punkt (0,1), y2(t) durch den Punkt (0,2) hindurch. ## 5. Grafische Darstellung der exakten L\366sung (2. M\366glichkeit) plot([z1,z2,t=0..2*Pi],thickness=4,color=black,scaling=constrained); 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 # Eingabe einer Funktion in Parameterdarstellung als Liste # Darstellung einer Phasenkurve in der z1,z2-Ebene. ## 6. Numerische L\366sung f:=dsolve({sy,y1(0)=1,y2(0)=2},{y1(t),y2(t)},numeric); 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 array([seq([t=n*0.2,y1=subs(f(n*0.2),y1(t)),y2=subs(f(n*0.2),y2(t))],
n=0..10)]);
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 ## 7. Grafische Darstellung der numerischen L\366sung (1. M\366glichkeit) p1:=odeplot(f,[t,y1(t)],0..4*Pi, thickness=4,color=black): p2:=odeplot(f,[t,y2(t)],0..4*Pi, thickness=4,color=black): display(p1,p2); 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 # display \374berlagert die Eizelgrafiken p1,p2 zu einer neuen Grafik. ## 8. Grafische Darstellung der numerischen L\366sung (2. M\366glichkeit) odeplot(f,[y1(t),y2(t)],0..2*Pi,thickness=4,color=black,
numpoints=500,scaling=constrained); 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# Darstellung einer Phasenkurve in der y1,y2-Ebene. ## 9. Grafische Darstellung der numerischen L\366sung (3. M\366glichkeit) odeplot(f,[t,y1(t),y2(t)],0..4*Pi,thickness=4,color=black,numpoints=500,axes=normal); 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#Darstellung der L\366sung als Raumkurve.