The simplest DEs — yet they model population growth, cooling, and mixing.
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(1/y) dy = x dx → ln|y| = x²/2 + C → y = Ae^(x²/2)
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The integrating factor technique converts a non-separable DE into an exact derivative. This method uses the product rule in reverse and relies on integration techniques.
Exactness connects to partial derivatives and conservative vector fields. Non-exact equations can sometimes be made exact with an integrating factor.