Initial Conditions and Separation of Variables
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Solve
d
y
d
x
=
y
\frac{dy}{dx} = y
d
x
d
y
=
y
for
y
(
0
)
=
2
y(0) = 2
y
(
0
)
=
2
. What is the particular solution?
QUESTION
Find
C
C
C
for the solution
y
=
C
e
3
x
y = Ce^{3x}
y
=
C
e
3
x
given
y
(
0
)
=
5
y(0) = 5
y
(
0
)
=
5
.
QUESTION
Find the particular solution of
d
y
d
x
=
4
y
\frac{dy}{dx} = 4y
d
x
d
y
=
4
y
with
y
(
1
)
=
3
y(1) = 3
y
(
1
)
=
3
.
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ANSWER
y
=
3
e
4
(
x
−
1
)
y = 3e^{4(x-1)}
y
=
3
e
4
(
x
−
1
)
. General solution
y
=
C
e
4
x
y = Ce^{4x}
y
=
C
e
4
x
, apply
y
(
1
)
=
3
y(1) = 3
y
(
1
)
=
3
to find
C
C
C
.
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