Equations Solvable for p, Math, Marketing Management

Equations Solvable for p, Math, Marketing Management

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Suppose the equation F (x, y, p, …., pn) = 0 on solving for p is expressible as

(p – ƒ1) (p – ƒ2) …. (p – ƒn) = 0,

Where ƒi’s are functions of x and y. Then

P – ƒi = 0, I = 1, 2, …., n

Or, dy/dx = ƒi(x, y), I = 1, 2, ….., n

which can be solved by the methods discussed earlier. If Øi (x, y, ci) = 0 is the solution of p – ƒi = 0 for i = 1, 2, …., n, the solution of the given differential equation is of the form

Ø1 (x, y, c1) . Ø2 (x, y, c2) ….. Øn (x, y, cn) = 0.

Since a differential equation of the first order has only one arbitrary constant, the general solution of the given equation will be of the form

Ø1 (x, y, c) . Ø2 (x, y, c) ….. Øn (x, y, cn) = 0.

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