As I wrote earlier, the inflection points of discrete data is not a well-defined concept.
The data that you have presented (which I see that you picked up from the Matlab
discussion on the web) is particularly ill-suited for assigning any meaningful sense

of inflection.  Here is what you can expect.

This is what the data looks like:

I don't see a meaningful way of assigning "inflection points" to that data.

Nevertheless, let's try fitting it with a 6th degree polynomial.

For whatever it's worth, the "inflection points" are at

Alternatively, you may try a spline fit:

The curve exhibits several inflection points.  But can we say those are the

inflection points of the data?  I would say not.  But if you insist, you may

obtain them by finding the roots of the curve's second derivative which

looks like this:

The graph of the function :

Animation of the disk's tenperature versus time:

Recover the coefficient matrix:

Alternatively, if the system is given as

Then we do

We look at all selections of , and pick  and .
That gives us 12 cases.  We evaluate  for those 12 cases and obtain a
linear system of 12 equations in the 6 unknowns .

i = 1, j = 1, h in {2}, k in {2, 3}
i = 1, j = 2, h in {2}, k in {1, 3}
i = 1, j = 3, h in {2}, k in {1, 2}
i = 2, j = 1, h in {1}, k in {2, 3}
i = 2, j = 2, h in {1}, k in {1, 3}
i = 2, j = 3, h in {1}, k in {1, 2}

We see that the system has no solution (it is inconsistent).  You need to reformulate
your question.

Solving statically determinate trusses in Maple

This worksheet shows how to solve a statically determinate truss in Maple.
It is done through an example but the method is general and applies to both
2D and 3D trusses.  With a little extra work it should be possible to encapsulate
the process into a general module.  I will leave that as an exercise for the interested
reader.

The example truss is taken from

http://adaptivemap.ma.psu.edu/websites/5_structures/method_of_joints/methodofjoints.html
                               

Rouben Rostamian
2019-11-06

Define the coordinates of the joints, taken from the picture above:

A member that connects joints i and j is represented as the pair

We precompute the lengths of the members because these will be needed in several places later on.

Force[i] is the force vector acting on the joint #i.  We do not distinguish between the given/applied
forces (in this case those acting on the joints #2 and #4) and the (unknown) reaction forces at the
supports.  Referring to the picture, we see that joint #1 is an anchor therefore its reaction has
both horizontal and vertical components ( but joint #6 is a rolling support therefore its
reaction has only a vertical component

Here are the components of the reaction forces:

We write  for the (yet unknown)  axial force within the member #i.  A positive
corresponds to tension while a negative   corresponds to compression.  Here is
the problem's complete set of unknowns:

We plot the truss to reassure ourselves that we have made no data entry errors

At this point we are done with setting up the problem.  Now we proceed with the solution.

The matrix  defined below expresses the connectivity of the truss.  Specifically,
if  is zero then the joints  and are not connected.  Otherwise they are
connected through the member .

This is what   looks like:

At equilibrium the resultant of forces applied to every joint
is zero.  This gives us a system of (2*nJoints) equations.

Here is the solution of truss

and here is the floating point representation of the solution:

Your system consists of four differential equations:

Differentiating de1 with respect to t we get

This says that either the first derivative or the second derivative of  is zero.

Let's look at the case where the first derivative of  is zero.

Then  is a constant.  But you want , therefore  is identically zero.
Then

from de1 we get
from de3 we get ;
from de2 we get
from de4 we get

Now, let's look at the case where the second derivative  is zero
Then  because you want .  The coefficient
is arbitrary.  Then

from de3 we get
from de4 we get ;
from de1 we get ;
from de2 we get .

Your eq41 is:

We see that the right-hand side is a function of , everything else being
constants. To simplify the computation, replace that messy expression with
a generic , as in

Then execute your worksheet to arrive at this simple representation of the solution:

To complete the calculation, you need to evaluate the integral in the denominator.
Since  is defined piecewise, there are too many cases if the parameters
and  are unspecified.  What do you know about how those parameters are related?
Perhaps with some a priori information on the relative values of the paramters a
general answer can be obtained.

In the absence of that information, specifying the parameters is the way to go.
For instance, with your choice of numerical values the integral evaluates to 100: