Hello, i have a very basic question. Regarding differential equations, we have s
ID: 2901390 • Letter: H
Question
Hello,
i have a very basic question. Regarding differential equations, we have studied the following: Laplace transform and inverse, annihilation and superposition, seperable equations, exact method, and solutions by substitution. My question is: WHAT DO ALL OF THESE METHODS HAVE IN COMMON? What do they lead to? Perhaps a better question maybe is what is your opinion of all of these methods that i have listed and what will they all lead to? Please be as detailed as possible. thanks for your input! i appreciate it!
Explanation / Answer
The fact that we have so many methods arises because we cannot solve all possible differential equations using the same method.
Substitution is used when substituting a particular function reduces the equation to a simpler form. Laplace is used when we know all the laplace transforms of the functions in the equation and we are able to find the resulting inverse.
So, there will be some equation which may not reduce with substitution and cannot be solved by Laplace and thus other methods are used. The common among all these methods is to make the solving of the differential equation easier
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