Initial Conditions and Separation of Variables
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the role of
C
C
C
in the solution
y
=
C
e
k
x
y = Ce^{kx}
y
=
C
e
k
x
?
QUESTION
Determine the general solution for
d
y
d
x
=
1
x
\frac{dy}{dx} = \frac{1}{x}
d
x
d
y
=
x
1
.
QUESTION
What is the general solution for
d
y
d
x
=
−
y
\frac{dy}{dx} = -y
d
x
d
y
=
−
y
?
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ANSWER
y
=
C
e
−
x
y = Ce^{-x}
y
=
C
e
−
x
. Standard exponential decay with rate
1
1
1
.
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