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Home » The antiderivative of \( 200e^0.05t \) is: - IX Labs

The antiderivative of \( 200e^0.05t \) is: - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Richtige Herleitung:
Homogene Lösung: $a_n^{(h)} = A \cdot 2^n$
Partikuläre Lösung: Konstant $C$, einsetzen: $C = 2C - 3 \Rightarrow C...
Allgemeine Lösung: $a_n = A \cdot 2^n + 3$
Nutze $a_0 = 5$: $5 = A + 3 \Rightarrow A = 2$
Also: $a_n = 2 \cdot 2^n + 3 = 2^{n+1} + 3$? Warte — Prüfe:
$a_0 = 2^1 + 3 = 5$, korrekt
$a_1 = 2^2 + 3 = 7$, aber aus Rekurs: $2 \cdot 5 - 3 = 7$, korrekt
Wait — Fehler im Vorgang:
$a_n = A \cdot 2^n + 3$

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