Solving a System of 2 ODES with Interval conditions (IVP)

In Progress

1. The problem statement, all variables and given/known data

I am trying to solve a system of 2 ordinary differential equations using matlab. However, I am not able to get numerical solutions from the code despite having keyed in all possible solutions.

2. Relevant equations

The equations I am given are:

dx/dt=A(x/t)+By

dy/dt=C(x/t^2)+D(y/t)

and the boundary conditions are:

y(1)=0; y(1.2)=-100E6

3. The attempt at a solution

My code so far:

%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)

eqns = [diff(x,t)==A*(x/t)+B*y, diff(y,t)==-C*(x/t^2)-D*y];

cond = [y(1) == 0, y(1.2)==-P];

withSimplifications = dsolve(eqns, cond)

withoutSimplifications = dsolve(eqns, cond, 'IgnoreAnalyticConstraints', false)

[xSol(t), ySol(t)] = dsolve(eqns)

The answer is get is

Warning: Explicit solution could not be found.

> In dsolve (line 201)

In IsotropicThickWallCylinder (line 18)

xSol(t) =

[ empty sym ]

ySol(t) =

[ empty sym ]

Would really appreciate some help.

Skills: Engineering, Mathematics, Matlab and Mathematica, Software Testing

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Project ID: #12240206

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