Q2.6 - 7EExpert-verified
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
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
It seems that the given equation is
Therefore, the given equation is the form of
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