Finding General Solutions: Separation of Variables
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Identify the integration:
y
d
y
=
x
d
x
y dy = x dx
y
d
y
=
x
d
x
.
QUESTION
What is the general solution for
d
y
d
x
=
2
x
\frac{dy}{dx} = 2x
d
x
d
y
=
2
x
?
QUESTION
What is the result of integrating
x
d
x
=
y
d
y
x dx = y dy
x
d
x
=
y
d
y
?
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ANSWER
x
2
2
=
y
2
2
+
C
\frac{x^2}{2} = \frac{y^2}{2} + C
2
x
2
=
2
y
2
+
C
. Both sides integrate to
x
2
2
\frac{x^2}{2}
2
x
2
and
y
2
2
\frac{y^2}{2}
2
y
2
respectively.
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