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Those useless transforms (are you referring to Laplace and friends?) are pretty useful in EE.

Yep, the transforms and series solutions are actually the most important part of ODEs, not just in EE but also in PDEs.

All fair criticisms, but I was recollecting on reading Boyce & DiPrima where the Laplace was relegated to IVP.

I was left with feeling that I had only learned yet another trick until I read Churchill & Brown's Complex Variables and Applications.