Expert: Paul Klarreich - 11/12/2011

Question
dy/dx=-xy^2 and y(1)=-.25

My work
(1/y^2)dy=-xdx

I then integrate to find
-y^-1=(-x^2/2)+C
C=9/2

-y^-1=(-x^2/2)+9/2
*this is where i am confused. What should I do next. My teacher told me the answer is y=2/(x^2-9). Please explain the process to me.

Answer
Questioner: Samantha
Country: Texas, United States
Category: Calculus
Private: No
Subject: Calculus
Question: dy/dx=-xy^2 and y(1)=-.25

My work
(1/y^2)dy=-xdx

I then integrate to find
-y^-1=(-x^2/2)+C

>>>>>>> which you should simplify: (makes life easier -- much)

- 1     - x^2
----- = ------  + C
 y       2

 1      x^2
----- = ------  + C   <<<< OK, OK, it's not the same C, but if you don't tell,...
 y       2

- 1      1^2
----- = ------  + C
1/4       2

       1
- 4 = -----  + C
       2
      9
C = - ---
      2

C=9/2   <<< not the same as your C, but...

Now you want:

 1      x^2       9
----- = ------  - ---
 y       2        2

 1      x^2 - 9
----- = ---------
 y         2   

Just invert, and....


My teacher told me the answer is y=2/(x^2-9).