Already searched and browsed multiple different threads and still cannot find a solution.

Apologizing the noob nature of this question.

In this code below, Why is the factor command not working?

Download factor_polynomial_2_multivariable.mwfactor_polynomial_2_multivariable.mw

Simple test of GaussianElimination function

Why doesn't this work? 

Also can I just confirm that for GaussianElimination (according to the help this uses LUDecomposition function with the output=['U'] option) the input is the augmented matrix of the system, the coefficient matrix augmented with the RHS)

In a separate test I got an example working using this code, but I've never seen this syntax before for A Matrix (using << it seems?)

Thank you for your help.

ORIGINAL ATTEMPT

Download gauss_elimination_2.mw

Trying to solve this IVP of the SHO  (second order linear costant-coefficient).

Everything works fine until I come to the solving even after using dsolve with initial conditions (even using the differential operator D in the initial conditions)  , the answer still contains _C1, an unknown constant.

The full worksheet is below.  The code for dsolve is:

sol3 := dsolve(subs(par1, {de1, D(x)*0 = 0, x(0) = 1}), x(t));

Hoping you can help with a solution.