Verifying Solutions for Differential Equations
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Verify if
y
=
1
1
−
x
y = \frac{1}{1-x}
y
=
1
−
x
1
is a solution to
y
′
=
y
2
y' = y^2
y
′
=
y
2
.
QUESTION
Is
y
=
e
3
x
y = e^{3x}
y
=
e
3
x
a solution to
y
′
=
3
y
y' = 3y
y
′
=
3
y
?
QUESTION
Is
y
=
x
2
−
4
x
y = x^2 - 4x
y
=
x
2
−
4
x
a solution to
y
′
′
=
2
y'' = 2
y
′′
=
2
?
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ANSWER
Yes, it is a solution.
y
′
=
2
x
−
4
y' = 2x - 4
y
′
=
2
x
−
4
,
y
′
′
=
2
y'' = 2
y
′′
=
2
, equation is satisfied.
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