MaplePrimes - answers and comments on Question, Differential equations solving and plotting

Numerical solution

Thomas Richard — Wed, 30 Jan 2013 18:42:26 Z

It seems only a numerical solution is feasible. Try this as a starting point for further investigations:

m := 5:
X := diff(F(t),t$2)+(10+8*sin(m*t)/(m*t))*F(t) = 0;
ics := F(0)=1,D(F)(0)=0;
sol_proc := dsolve([X,ics],numeric);
plots:-odeplot(sol_proc,t=0..10);

Numeric solution

Preben Alsholm — Wed, 30 Jan 2013 18:46:20 Z

For a numerical solution m and initial conditions must have numerical values:

X := diff(F(t), t$2)+(10+8*sin(m*t)/(m*t))*F(t) = 0;
T:=2*Pi: #Change as desired
res:=dsolve({eval(X,m=1),F(0)=1,D(F)(0)=0},numeric,range=T);
plots:-odeplot(res,[t,F(t)],0..T,refine=1);

Generalization

Markiyan Hirnyk — Wed, 30 Jan 2013 18:50:22 Z

> X := diff(F(t), `$`(t, 2))+(10+8*sin(m*t)/(m*t))*F(t) = 0;
> sol := dsolve({eval(X), F((1/2)*Pi) = a, (D(F))((1/2)*Pi) = b}, numeric, parameters = [a, b, m], output = listprocedure);
> sol(parameters = [1, -2, 1]);
> plots:-odeplot(sol, t = 0 .. 2*Pi);