lecture_24 (dragged) 3

lecture_24 (dragged) 3 - P 1 t P t W 1 W dW dt = − P 1 t...

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4 MA 36600 LECTURE NOTES: FRIDAY, MARCH 13 since the n th row is equal to the ( k + 1)st row for k =0 , 1 ,..., ( n 2). Finally, to ±nish o² the proof of Abel’s Theorem, we ±nd the general solution to this ±rst order di²erential equation: W (1) =
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Unformatted text preview: P 1 ( t ) P ( t ) W 1 W dW dt = − P 1 ( t ) P ( t ) ln | W ( t ) | = − ° t P 1 ( τ ) P ( τ ) dτ + C 1 = ⇒ W ( t ) = C exp ± − ° t P 1 ( τ ) P ( τ ) dτ ² where we have set C = ± e C 1 as a constant....
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