Maple-Worksheet: Differentialgleichungen

Einführung in Maple Übungen

Mathematik

Differentialgleichungen

restart;

>	DGl1:= diff (f(x), x) = f(x);

Lösung der Differentialgleichung DGl1:

>	dsolve (DGl1 , f(x));

Die Probe:

>	f:= x -> a*exp(x); Df:= D(f);

Lösung der Gleichung DGl1 unter Beachtung der Bedingung f(2) = 4:

>	f:= 'f': dsolve ({DGl1, f(2.0) = 4}, f(x));

f(x) = 4/exp(2)*exp(x)

>
evalf (%, 4);

restart;

>	DGl2:= diff (f(t), t) = kf(t)(S - f(t));

>
dsolve (DGl2, f(t));

f(t) = S/(1+exp(-k*S*t)*_C1*S)

>
f:= t -> 100/(1 + 200*exp(-4*t));

>
plot (f(t), t = 0..3);