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The day I realized Laplace transforms converted difficult linear differential equations into simple algebra problems was the day I began to appreciate Laplace transforms.

Brian Douglas produced a decent set of lectures on control systems, I found them to be quite useful during my degree: https://www.youtube.com/@ControlLectures

It’s definitely worth persisting with the Laplace transform.. you get a ton of stuff you can do when you have H(s)=Y(s)/X(s)