Hello, As of recently, I've been working with Laplace transforms and have a question about their relationship to solving differential equations. I know the definition of the laplace transform and I know that a function is essentially being transformed from the time domain to complex frequency domain. I also know that they are a useful tool in solving differential equations. They essentially replace solving a differential equation with a simple algebraic equation. However, my question is why? I don't completely understand how this occurs and I don't think I have ever been told exactly why this is true. I mean, what if we were to make up some transformation other than the Laplace and apply that to a differential equation. Why couldn't we solve a differential equation with that? Is there any good explanation out there for this?