“Bernoulli Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Bernoulli Differential Equation

释义

Bernoulli Differential Equation

(1)

Let

for

, then

(2)

Rewriting (1) gives

(3)

Plugging (3) into (2),

(4)

Now, this is a linear First-Order Ordinary Differential Equationof the form

(5)

where

and

. It can therefore be solved analytically using an Integrating Factor


			(6)

where

is a constant of integration. If

, then equation (1) becomes

(7)

(8)

(9)

The general solution is then, with

and

constants,

(10)

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