Question

In problems identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form .

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Short answer

The given equation is the form of Bernoulli equation.

Step-by-step solution

General form of homogeneous, Bernoulli, linear coefficients of the form of

• Homogeneous equation

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.

• Bernoulli’s equation

A first-order equation that can be written in the form , where and are continuous on an interval and is a real number, is called a Bernoulli equation.

• Equation of Linear coefficients

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 bothandinto new variables, sayand. This is the situation for equations with linear coefficients-that is, equations of the form

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Evaluate the given equation

Given, .

By Evaluating,

Comparing with general form of Bernoulli equation it seems that the given equation also Bernoulli equation.

Therefore, the given equation is the form of Bernoulli equation.