with(DEtools):Uebung 3.13a)DEplot(diff(y(x),x)-(2+x)*y(x)=0, y(x), x=-4..2, y=-1..3, [[y(0)=exp(1)]]);# allgemeine Lsg:
dsolve(diff(y(x),x)-(2+x)*y(x)=0, y(x));# spez. Lsg:
l_spez := simplify(dsolve({ diff(y(x),x)-(2+x)*y(x)=0, y(0)=exp(1) }, y(x)));l_spez2:=x -> exp(1+2*x+1/2*x^2);
plot(l_spez2(x), x=4..5);3b)restart:
with(DEtools):
infolevel[dsolve]:=3;dgl:=diff(y(x),x)=2*sqrt(y(x)), y(x);eigenschaften:=odeadvisor(dgl);
separierbar:=odeadvisor(dgl,[separable]);DEplot(diff(y(x),x)=2*sqrt(y(x)), y(x), x=-2..5, y=-1..2, [[y(1)=4]]);# allgemeine Lsg:
dsolve(diff(y(x),x)=2*sqrt(y(x)), y(x) );# spez. Lsg:
l_spez := simplify(dsolve({ diff(y(x),x)=2*sqrt(y(x)), y(1)=4 }, y(x)));#y=(x+1)^26)a)dgl:=diff(y(x),x)=y(x)/2*(x-sqrt(x)), y(x);eigenschaften:=odeadvisor(dgl);
separierbar:=odeadvisor(dgl,[separable]);simplify(dsolve(dgl));