Discussion
Match the first-order equation with the method it calls for. 1. \( dy/dx = f(x)g(y) \) 2. \( dy/dx + Py = Q \) 3. \( dy/dx + Py = Qy^{n} \) P. Integrating factor Q. Separation of variables R. Substitution \( v = y^{1-n} \)
Answer: D
A product of a function of each variable separates directly. The linear form takes an integrating factor built from the coefficient of \( y \). Bernoulli's form is neither, but the substitution \( v = y^{1-n} \) turns it into the linear case, after which the integrating factor applies
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