Consider the differential equation dy/dx = y^2 and answer the following:

Show that the family of functions y = 1/C-x are solutions to the differential equation dy/dx =y^2 .

I have been taking Calc entirely online and this is the first time I feel like I followed the instructors youtube videos and was unable to do the homework.'

I of course can just be dumb.

I believe I am supposed to find the derivative of (1/C-x) and then plug that result in for y in dy/dx=y^2.

I do need help in getting the answer, but I was hoping you could recommend the general process or any resources that could help me understand.

1:43 PM Sun Oct 10 . . . 34% 88 Q n D Untitled Notebook X . .. 2 Back.. C$162 Lab2 Exerc... x CS162 Lab2 Practi. x Untitled Notebook x Section 7.2 - Direc.. x Section 7.1 - Mode.. Untitled Noteb... W. g ' ( x ) fly ) - f ( x ) g (x ) 3. Show that the family of functions y = - are solutions to the differential equation - 1 = yz. C-x dx Show all of your work in an organized manner. dy - ( C + 1 ) . 1 - (0 ) ( c-x ) - C+ 1 of x (c- x ) ? ( C - x ) ? e ( c - x ) 2 - ( C + 1 ) (c - x ) 4 4. Show that y = 0 is an equilibrium solution to -,= y' . How is this also apparent in the direction dx field? Page 2 of 3