Two-Point Boundary Value Problem

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Ketav Majumdar
Ketav Majumdar on 2 Dec 2016
Commented: Torsten on 5 Dec 2016
Hi there, I am currently trying to solve a two point boundary value problem for a system of 2 ordinary linear differential equation.
dx/dt=A(x/t)+By dy/dt=C(x/t^2)+D(y/t)
B.C y at 1=10 and y at 2=0
I have terrible matlab experience and knowledge.
This is my code so far (It doesnt work)
if true
% %Mechanical Properties of Material
E=200e9;
nu=0.3;
P=100E6;
%Constants A,B,C,D in the Equations
a11= (1/E);
a12= (-nu/E);
a33= (1/E);
A= (a12)/(a11+a12);
B= ((a33)-((2*a12^2)/(a11+a12)));
C= (a11)/(a11^2-a12^2);
D= (2*a12+a11)/(a11+a12);
%Defining the System of 2ODES
syms x(t) y(t)
t=1;
eqns = [diff(x,t)==A*(x/t)+B*y, diff(y,t)==-C*(x/t^2)-D*y];
cond = [y(0) == 0, y(1.2)==-P];
withSimplifications = dsolve(eqns, cond)
withoutSimplifications = dsolve(eqns, cond, 'IgnoreAnalyticConstraints', false)
[xSol(t), ySol(t)] = dsolve(eqns, cond)
end
Would anyone be able to give me any solutions to this problem?
  6 Comments
Torsten
Torsten on 5 Dec 2016
with
U=2-D-A and V=-D+A*D-B*C
gives the solution for y.
Then
x = 1/C*t^2*dy/dt-D/C*t*y
gives the solution for x.
Best wishes
Torsten.

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Answers (1)

Tamir Suliman
Tamir Suliman on 3 Dec 2016
You will have to differneitate then solve Since
x'=A(x/t)+By --- differnetiate A(x/t)+By for y relative to t
Y' = A*(x *-1/t^2 +1/t*x' ) + BY'
at t= 1 Y =10 at t =2 y = 0
(1-B)*C(x/t^2) + D (y/t) = A*(x *-1/t^2 +1/t*x' )
sub y =10 then solve for t =1 again sub y = 0 then solve for t =2
then use diff and dsvolve with t = 1 and t =2

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