Finding General Solutions: Separation of Variables
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
Card 1
of 14
0 got it
0 to review
Current
Got it
Still learning
Not seen
QUESTION
What is the result of integrating
e
−
y
d
y
=
x
d
x
e^{-y} dy = x dx
e
−
y
d
y
=
x
d
x
?
QUESTION
Separate variables and integrate:
d
y
d
x
=
2
x
y
\frac{dy}{dx} = \frac{2x}{y}
d
x
d
y
=
y
2
x
.
QUESTION
Identify the error:
d
y
d
x
=
x
2
y
\frac{dy}{dx} = x^2y
d
x
d
y
=
x
2
y
rewritten as
y
d
y
d
x
=
x
2
y \frac{dy}{dx} = x^2
y
d
x
d
y
=
x
2
.
Tap to flip before you grade
ANSWER
Correct:
1
y
d
y
=
x
2
d
x
\frac{1}{y} dy = x^2 dx
y
1
d
y
=
x
2
d
x
. Variables must be properly separated before integrating.
Swipe → got it · swipe ← still learning
Got it
Still learning
Flip Card
Previous card
Next card