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Solving a EDO by algebra

  1. Dec 14, 2013 #1
    I was reading and searching about a theory that originated the laplace transfom (http://en.wikipedia.org/wiki/Operational_calculus), but I don't know very well, second this theory, is possible to solve a differential equation only with algebric artifices (see http://es.wikipedia.org/wiki/Transformada_de_Laplace#Perspectiva_hist.C3.B3rica). But, is really possible?
    attachment.php?attachmentid=64789&stc=1&d=1387061544.jpg
    Do you could show me some algebric artifice (step by step) that solve this EDO??
     

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