In problems 1-8 identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form .
The given equation is the form of both homogeneous and Bernoulli.
If the right-hand side of the equation can be expressed as a function of the ratio alone, then we say the equation is homogeneous.
Equations of the form When the right-hand side of the equation can be expressed as a function of the combination where and are constants, that is, then the substitution transforms the equation into a separable one.
A first-order equation that can be written in the form , where and are continuous on interval and localid="1654934017689" is a real number, is called a Bernoulli equation.
We have used various substitutions for to transform the original equation into a new equation that we could solve. In some cases, we must transform both and into new variables, say and . This is the situation for equations with linear coefficients-that is, equations of the form
role="math" localid="1654934940793" .........(1)
Let us consider
From Equation (1),
So, the given equation is homogeneous.
It can be rewritten as,
Comparing the found equation with Bernoulli general form of equation. It seems that the given equation is Bernoulli equation as well.
Therefore, the given equation is the form of both homogeneous and Bernoulli.
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