Question

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

Short answer

The given equation is the form of linear coefficients.

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

.

Evaluate the given equation

Given,

By Evaluating,

Since,

The given equation satisfies .

Therefore, the given equation is the form of a linear coefficient.