Section 2.2 Question 30 part c and d

[anikal2001]

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]

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]

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]

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.