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Implicit differentiation dy/dx=xy^2

  • Thread starter mandymanny
  • Start date
  • #1

Homework Statement


If dy/dx=xy^2 and x=1 when y=1, then y=

(A) x^2
(B) -2/(x^2 -3)
(C) x^2 + 3
(D) 2/(x^2 +1)
(E) (x^2 -3)/2


Homework Equations





The Attempt at a Solution



dy/dx=xy^2
dy=xy^2dx
dy/y^2=x dx
∫dy/y^2=∫x dx
-1/y = x^2/2 + C
y=-2/x^2 + C
1=-2/1^2 + C
C=3
y=-2/x^2 +3

but thats not the answer...

please help i have the AP test tomorrow.
thanks
much appreciated
 

Answers and Replies

  • #2
Vid
401
0
Watch the step between line 5 and 6. f(x) = x^-1 is not linear.
 
  • #3
1,341
3
That's not really implicit differentiation -- it's a diff. eq.
 
  • #4
yes?

when i integrate, it's y^-1/-1 right? not just y^-1
??
 
  • #5
Nevermind I got it.
Answer is B :)
 

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