Given below is a problem where it is shown that proper modeling is key to solving engineering problems. An improper model and a proper model may lead to opposite conclusions
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Author: Autar Kaw
Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.
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The Numerical Methods Guy 
Dear Professor Autar Kaw,
I agree with you that not all of mathematics model can be solved exactly in analytical form. In this address :
http://math152.wordpress.com/2008/12/07/the-stochastic-group/#comment-242
there are several first order ODE that require implementation of your numerical schemes.
Hopefully this information useful for all visitors here.
Sincerely yours,
Rohedi.
Physics Dept, Faculty of Natural Sciences,
Sepuluh Nopember Institute of Technology (ITS) Surabaya, Indonesia.
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