- #1
alane1994
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I have several examples in my book for this problem, but I don't understand what they are saying. I guess I don't get the format. I will post up the example I think applies to the problem, and if one of you could explain the example that would be fantastic.
Determine whether each of the equations is exact. If it is exact, find the solution.
This is my problem.
Example Problem.
Solve the differential equation
The equation is neither linear nor separable, so the methods suitable for those types of equations are not applicable here. However observe that the function has the property that
Therefore, the differential equation can be written as
Assuming that y is a function of x, we can use the chain rule to write the left side of Eq.3 as . Then Eq.3 has the form
By integrating Eq.4 we obtain
where c is an arbitrary constant. the level curves of are the integral of curves of Eq.1. Solutions of Eq.1 are defined implicitly by Eq.5.
My main questions are what is with the notation of ?
And, just some clarification would be fantastic.
Determine whether each of the equations is exact. If it is exact, find the solution.
This is my problem.
Example Problem.
Solve the differential equation
The equation is neither linear nor separable, so the methods suitable for those types of equations are not applicable here. However observe that the function
Therefore, the differential equation can be written as
Assuming that y is a function of x, we can use the chain rule to write the left side of Eq.3 as
By integrating Eq.4 we obtain
where c is an arbitrary constant. the level curves of
My main questions are what is with the notation of
And, just some clarification would be fantastic.