Solving Exact Equations

Category: Differential Equations

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Solve for the solution for

Solution:

The first thing that we have to do is to check the above equation if it is exact equation or not as follows

Let 

then 

Let 

then

Since

then the given equation is Exact Equation. The solution for the above equation is F = C. Consider the given equation

Let 

and

Integrate the partial derivative of the first equation above with respect to x, we have

Since we are integrating the partial derivatives, then another unknown function, T(y) must be added.  If 

then

To solve for T'(y), equate

Since the arbitrary constant is already included in F = C, then we don't have to add the arbitrary constant in the above equation. Therefore,

Therefore, the general solution is