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 Bernoulli 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 a and b 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 P(x) and Q(x) are continuous on an interval (a, b) and n is a real number, is called a Bernoulli equation.
We have used various substitutions for y to transform the original equation into a new equation that we could solve. In some cases, we must transform both x and y into new variables, say u and v. This is the situation for equations with linear coefficients-that is, equations of the form
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.
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