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[Music] dr rico here this is a lecture from my course system dynamics the syllabus link is in the description [Music] all right welcome to laplace transforms chapter lecture solving input output odes with laplace transforms and their inverses so lets begin laplace transforms provide a convenient method for solving input output which we denote io ordinary differential equations or odes consider a dynamic system described by the iode with time t output y input u constant coefficients a and b order and m less than n m and n being integers as this time derivatives of the output on the left-hand side of the equation time derivatives of the input on the right hand side here we go rewritten in summation form you never thought you would like summation form so much here it is a little bit simpler were summing coefficients a i times the derivatives of y where were using lagranges notation okay lagranges notation begins with the primes and then as you go to higher primes and you run out of
