# Toronto Math Forum

## MAT244--2020F => MAT244--Lectures & Home Assignments => Chapter 2 => Topic started by: anikal2001 on September 22, 2020, 06:03:47 PM

Title: Section 2.2 Question 30 part c and d
Post by: anikal2001 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
Title: Re: Section 2.2 Question 30 part c and d
Post by: Jing_Wang 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 ;)
Title: Re: Section 2.2 Question 30 part c and d
Post by: YuyingC 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")
Title: Re: Section 2.2 Question 30 part c and d
Post by: anikal2001 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.