Question: Dslove numeric with know function

Hi,

according to my previous question

http://www.mapleprimes.com/questions/201435-ODE-With-Constraint

I wrote the following code. at first, the code solve the equation for f and when it slves that, I want to solve Theta in such a way that use the values of f in previous calculation. I use the command 'known' but i couldnt find thesolution

I would be most grateful if you could help me in this problem

Thanks for your attentions in advance

restart; # Notice that Restart (capital R) has no effect (to catch that use semicolon, not colon)
a:=0.13:
b:=0.41:
reynolds:=1.125*10^7;  
Eq1:=diff(f(x),x$3)+diff(f(x),x$2)*f(x)+b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)^2*x^2,x$1);
Eq2:=diff(g(x),x$3)+diff(g(x),x$2)*g(x)+c*a^2*sqrt(2*reynolds)*diff(diff(g(x),x$2)^2*x,x$1);
eq1:=isolate(Eq1,diff(f(x),x,x,x));
eq2:=subs(g=f,isolate(Eq2,diff(g(x),x,x,x)));
EQ:=diff(f(x),x,x,x)=piecewise(x<c*0.1,rhs(eq1),rhs(eq2));


c:=75:
;
Q:=proc(pp2) local res,F0,F1,F2;
print(pp2);
if not type(pp2,numeric) then return 'procname(_passed)' end if:
res:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=pp2},numeric,output=listprocedure);
F0,F1,F2:=op(subs(subs(res),[f(x),diff(f(x),x),diff(f(x),x,x)])):
F1(c)-1;
end proc;


fsolve(Q(pp2)=0,pp2=(0..102));
se:=%;
res2:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=se},numeric,output=listprocedure);
G0,G1,G2:=op(subs(subs(res2),[f(x),diff(f(x),x),diff(f(x),x,x)])):

plots:-odeplot(res2,[seq([x,diff(f(x),[x$i])],i=0..2)],0..2); #This plots from and past 0.1*c
pr:=1;
prt:=0.89;

Eq11:=diff(theta(x),x$2)+pr*diff(theta(x),x$1)*f(x)+pr/prt*b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(theta(x),x$1)*x^2,x$1);
Eq22:=diff(g(x),x$2)+pr*diff(g(x),x$1)*f(x)+pr/prt*a^2*c*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(g(x),x$1)*x^1,x$1);
eq11:=isolate(Eq11,diff(f(x),x,x));
eq22:=subs(g=theta,isolate(Eq22,diff(g(x),x,x)));
EQT:=diff(theta(x),x,x)=piecewise(x<c*0.1,rhs(eq11),rhs(eq22));


QT:=proc(pp3) local res3,theta0,theta1;
print(pp3);
if not type(pp3,numeric) then return 'procname(_passed)' end if:
res3:=dsolve({EQT,theta(0)=1,D(theta)(0)=pp3,known=f},numeric,output=listprocedure);
theta0,theta1:=op(subs(subs(res),[theta(x),diff(theta(x),x)])):
theta0(c);
end proc;

fsolve(QT(pp3)=0,pp3=(0..200));
res3(0);

Amir