I keep getting “Separation of variables” questions wrong in Differential Equations. What's the trap?
integrating before separating the variables.
The usual trap: integrating before separating the variables. How to avoid it: get all y with dy and all x with dx, then integrate both sides. Go back to the definition — if you can write dy/dx = g(x)·h(y), gather all y-terms on one side and x-terms on the other, then integrate.
Key point
Separation of variables
Common mistake
integrating before separating the variables.
Memory tip
get all y with dy and all x with dx, then integrate both sides.
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