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

.

Given,

By Evaluating,

Since,

The given equation satisfies .

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