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.
I had trouble uploading the .mw file so I have included an alternative link to retrieve the file if the code contents is illegible or you cannot dowlad the file drectly from the weblink Download coeffs_of_homogen_soln_discrepancy.mw. You should be able to download from the alternative link below once you paste the link into your browser. If you cannot & wish for me to provide the file in some other fashion respond with some specific instructions & I will attempt to get the file to you.
Thanks 4 any help you can provide.