User talk:EGM6321.F12.team5.nguyen R4-1

Given
Considering the following ODE Sec21.

Find
Verify the exactness of ($$).

Solution
For an equation to be exact, it must satisfy two conditions Sec16. 1st Exactness Condition for N2-ODEs: The N2-ODE must have the particular form:

where

To reduce the order of the equation, we can use the following substitutions

to rewrite($$) in reduced order form.

From inspection, we can identify the following:

Therefore ($$) satisfies the 1st Exactness Condition. 2nd Exactness Condition for N2-ODEs: The N2-ODE must satisfy the following conditions:

Evaluating the derivatives of $$ f(x,y,p) $$ and $$ g(x,y,p) $$ from ($$) and ($$) we can evaluate the 2nd Exactness conditions ($$) and ($$) as follows

Conclusion Since the second exactness condition was not satisfied in ($$), we can conclude that this N2-ODE is not exact.