Expert: Paul Klarreich - 4/19/2007

Question
if dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=

Answer
Questioner:   tina
Category:  Calculus
 
Subject:  calculus
Question:  if dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=
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Hi, Tina,

If dy/dx=2y^2, then you can separate the variables:

dy
--- = 2dx
y^2

y^-2 dy = 2dx

Integrate:

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

-1
--- = 2x + C
y

Now put  y = -1  and  x = 1:

-1
-- = 2(1) + C
-1

1 = 2 + C
C = -1

The equation is

-1
--- = 2x - 1
y

Now if x = 2:

-1
--- = 2(2) - 1
y

-1
--- = 3
y

y = -1/3