Laplace Transforms
As early as 1744, Euler, followed by Lagrange, had started looking for solutions of differential equations in the form:
In 1785, Laplace took the key forward step in using integrals of this form in order to transform a whole difference equation, rather than simply as a form for the solution, and found that the transformed equation was easier to solve than the original.
Read more about this topic: Pierre-Simon Laplace
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