### Author Topic: Section 2.2 Question 30 part c and d  (Read 1957 times)

#### anikal2001

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##### Section 2.2 Question 30 part c and d
« on: September 22, 2020, 06:03:47 PM »
Hi can someone please explain how to do part b and c for question 30? I specifically am not able to understand how to express dy/dex in terms of x v and dv/dx. Part c gives a little bit of a hint, but I am unable to understand how they got there
Thanks

#### Jing_Wang

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##### Re: Section 2.2 Question 30 part c and d
« Reply #1 on: September 23, 2020, 08:59:09 AM »
b. y=v·x as given. Use multiplication rule for y' (with respect to dx):
y' = (v·x)' = (v')·x + v·(x') = x·v' + v.
c. The first equation follows immediately from (b). Eqs. (31) is obtained by moving v to the other side.
Hope this helps

#### YuyingC

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##### Re: Section 2.2 Question 30 part c and d
« Reply #2 on: September 23, 2020, 03:09:21 PM »
I also have a question related to a) for this exercise. Why is equation i called homogenous?
(I am sorry if this question is considered as "hijack topic")

#### anikal2001

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##### Re: Section 2.2 Question 30 part c and d
« Reply #3 on: September 23, 2020, 07:23:43 PM »
Its considered homogeneous because dy/dx=f(x,y) can be expressed as a function of the ration y/x only. This property is further discussed in the later chapters.