Implicit differentiation dy/dx=xy^2

[mandymanny]

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

 

[Vid]

Watch the step between line 5 and 6. f(x) = x^-1 is not linear.

 

[Feldoh]

That's not really implicit differentiation -- it's a diff. eq.

 

[mandymanny]

yes?

when i integrate, it's y^-1/-1 right? not just y^-1
??

 

[mandymanny]

Nevermind I got it.
Answer is B :)