Symbol Manipulation
Suppose we want to solve the differential equation
Treating these symbols as ordinary algebraic ones, and without giving any justification regarding the validity of this step, we take reciprocals of both sides:
Now we take a simple antiderivative:
Because this is a formal calculation, we can also allow ourselves to let and obtain another solution:
If we have any doubts about our argument, we can always check the final solutions to confirm that they solve the equation.
Read more about this topic: Formal Calculation, Examples
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