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The problem is this, we are solving differential equations using the LaPlace Transform for differential equations with non-constant coefficients. So on the board he does the LaPlace transform just fine, but when it comes to partial fractal decomposition to solve the actual differential equation he insists that if the factor in the denominator is a prime quadratic we do not need an Ax+B term. He says that unlike in calculus where we wanted to integrate something that we only need a constant term. This to me seems to be completely ludicrous because you cannot set two things equal which are not equal so when you solve the inverse LaPlace you get an answer that is not relevant to your initial problem.

Firstly, I am correct that you are not allowed to do what he is doing (throwing away the Ax term) and secondly, if so how do I tell him without upsetting him.