Modified D'Alembert's Principle Inquiry

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So I had been handed a differential equation to describe a "fluid's" motion ("fluid" because we are actually talking about plasma) inside the sun. I quickly digress to mention the frustrations of trying to type a mathematical equation into this this thing. The differential equation is as follows. It is very similar to the D'Alembert's Principle, but with the addition of the second derivative with respect to position it has thrown off my approach a couple of times. I was wondering if there exist a Modified D'Alembert's Principle where it takes into account that b != 0.