Implicit differentiation dy/dx=xy^2

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Homework Help Overview

The problem involves implicit differentiation of the equation dy/dx = xy^2, with a specific condition given for x and y. Participants are exploring the implications of this differential equation and attempting to find a function y in terms of x.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integration steps taken to solve the differential equation and question the validity of certain transformations. There is also a clarification sought regarding the nature of the equation and the integration process.

Discussion Status

The discussion includes attempts to derive a solution, with some participants providing feedback on the steps taken. There is an indication that one participant believes they have arrived at a correct answer, though this is not universally accepted or confirmed by others.

Contextual Notes

One participant mentions an upcoming AP test, indicating a time constraint and the pressure to understand the material quickly. There is also a note of confusion regarding the integration process and the classification of the equation as a differential equation rather than a straightforward implicit differentiation problem.

mandymanny
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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 that's not the answer...

please help i have the AP test tomorrow.
thanks
much appreciated
 
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Watch the step between line 5 and 6. f(x) = x^-1 is not linear.
 
That's not really implicit differentiation -- it's a diff. eq.
 
yes?

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

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