User:Cloudwu890202/Report2

Problem 5:Find the 1st derivative of a function and show that this function is N1-ODE
Report problem 2.5 from lecture notes section 9-2.

Given: A specified function
A specified function is shown as below:

Find: The 1st derivative of the function and show that it is a N1-ODE
Find the 1st derivative of ($$):

and show it is a N1-ODE.

Solution: the 1st derivative of this function has the same form with the N1-ODE

 * {| style="width:100%" border="0"

This solution was prepared without referring to previous solutions.
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * }

Find the first derivative by applying chain-rule to $$\displaystyle\phi(x,y)$$ ($$):

on the left side, the derivative can be written as

on the right side, the derivative can be written as

In this specified problem, the equation can be calculate as below

after observation, it can be found that ($$) has the same form as the particular class of N1-ODE which is showed as below

Thus, ($$) can be rewritten as below

Then build the relationship between ($$) and (5.7)($$):

apparently, the equation

has the same form with the a N1-ODE:

Thus, it has fulfilled the requirement to be a N1-ODE