AP Calculus AB Quiz
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DIFFERENTIAL EQUATIONS
Question 1
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Does
y
=
x
y=\sqrt{x}
y
=
x
satisfy the differential equation
d
y
d
x
=
1
2
x
\dfrac{dy}{dx}=\dfrac{1}{2\sqrt{x}}
d
x
d
y
=
2
x
1
for
x
>
0
x>0
x
>
0
?
A
No, because
y
′
=
1
x
y'=\dfrac{1}{\sqrt{x}}
y
′
=
x
1
but the right side is
1
2
x
\dfrac{1}{2\sqrt{x}}
2
x
1
.
B
Yes, because
y
′
=
1
2
x
y'=\dfrac{1}{2\sqrt{x}}
y
′
=
2
x
1
and the right side matches.
C
No, because
y
′
=
1
2
x
y'=\dfrac{1}{2x}
y
′
=
2
x
1
but the right side is
1
2
x
\dfrac{1}{2\sqrt{x}}
2
x
1
.
D
Yes, because
y
′
=
x
y'=\sqrt{x}
y
′
=
x
equals
1
2
x
\dfrac{1}{2\sqrt{x}}
2
x
1
.
E
No, because
y
′
=
2
x
y'=2\sqrt{x}
y
′
=
2
x
but the right side is
1
2
x
\dfrac{1}{2\sqrt{x}}
2
x
1
.
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