Use Taylor's Theorem to Find the First Five Terms of the Series

question 25

Multiple Choice

Use Taylor's Theorem to find the first five terms of the series solution of $y ^ {t} + ( 2 x - 1 ) y = 0$ given the initial condition $y ( 0 ) = 2$

• A)
• \[y = 2 - x + \frac { x ^ { 2 } } { 2 } - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 4 } } { 4 } + \cdots\]
• B)
• \[y = 2 - \frac { 2 } { 1 ! } x + \frac { 6 } { 2 ! } x ^ { 2 } - \frac { 10 } { 3 ! } x ^ { 3 } + \frac { 6 } { 4 ! } x ^ { 4 } + \cdots\]
• C)
• \[y = \frac { 2 } { 1 ! } x - \frac { 2 } { 2 ! } x ^ { 2 } - \frac { 10 } { 3 ! } x ^ { 3 } + \frac { 2 } { 4 ! } x ^ { 4 } - \frac { 2 } { 5 ! } x ^ { 5 } + \cdots\]
• D)
• \[y = 2 + \frac { 2 } { 1 ! } x - \frac { 2 } { 2 ! } x ^ { 2 } - \frac { 10 } { 3 ! } x ^ { 3 } + \frac { 2 } { 4 ! } x ^ { 4 } + \cdots\]
• E)
• \[y = 2 + x - \frac { x ^ { 2 } } { 2 } - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 4 } } { 4 } + \cdots\]

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