## Resolving coefficients to a 2nd order diff eq disc...

I resolved the coefficients to a 2nd order diff eq of the form:ay''+by'+cy=f(t)

I have included the .mw file for convenience at the link at the bottom of the page.  I resolved the coefficients in 2 different ways & they do not concur.  The 1st approach used the LaPlace transform & partial fraction decomposition.  The coefficient results are given by equations # 14 & 15.  The 2nd approach used undetermined coefficients where I assumed the particular solution and then applied the initial conditions to resolve the coefficients pertaining to the homogeneous solution which are given in the results listed in equation #23.  Noted in the 1st case the coeff's are A3 & A4 and for the 2nd approach the coeff's are A1 & A2.  I have worked this numerous times & do not understand why they do not concur.  So I thought I should get some fresh eyes on the problem to find where I may have gone wrong.

Any new perspective will be greatly apprecieated.

https://unl.box.com/s/dywe90wwpy0t4ilkuxshkivz2z26mud8

## multivariate partial fractions...

Has anyone been able to do multivariate partial fraction decomposition in maple (here is a paper introducing the idea https://arxiv.org/pdf/1206.4740.pdf)

I often find maple generating complicated rational functions that it would be nice to visualise in other ways

Here is an example of such a function if anyone wants to have a play:

(a*x^3+b*x*y^2+a*x*y+b*y^2)

/(a*x^3+a*b*x*y^2+a*b*y*x^2+b*y^3)

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