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If yes, what would it look like?

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    Although this video might not help you exactly understand visually what it is, this introduction will really help you understand why the Laplace transform is useful and why it is used: https://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/2017-02-19

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