AP Calculus AB Quiz
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DIFFERENTIAL EQUATIONS
Question 1
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A quantity
y
y
y
changes with
x
x
x
by
d
y
d
x
=
3
x
y
\dfrac{dy}{dx}=\dfrac{3}{x}y
d
x
d
y
=
x
3
y
. What is the general solution?
A
y
=
3
ln
∣
x
∣
+
C
y=3\ln|x|+C
y
=
3
ln
∣
x
∣
+
C
B
ln
∣
y
∣
=
3
x
+
C
\ln|y|=\dfrac{3}{x}+C
ln
∣
y
∣
=
x
3
+
C
C
y
=
C
x
3
y=Cx^{3}
y
=
C
x
3
D
y
=
x
3
y=x^{3}
y
=
x
3
E
y
=
C
ln
∣
x
3
∣
y=C\ln|x^{3}|
y
=
C
ln
∣
x
3
∣
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