- #1

Ketav

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## Homework Statement

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.

## Homework 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

## The Attempt at a Solution

**Mod note**: Added code tags.

My code so far:

Matlab:

```
%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.

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