Calculus
SOLUTION: Cypress College Calculus Questions
SOLUTION: Cypress College Calculus Questions.
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1. Problem 1
? ′ + ?? = 100?
Find the integrating factor for a form:
? ′ + ?(?)? = ?(?)
Such that:
?2
? = ? ∫ ?(?)?? = ? ∫ ??? = ? 2
Multiply both sides by the integrating factor:
?2
?2
?2
? 2 ? ′ + ? 2 ?? = 100?? 2
Rewrite the left side using the reverse product rule:
?2
′
?2
(? 2 ?) = 100?? 2
?2
?2
? (? 2 ?) = 100?? 2 ??
Integrate both sides:
?2
?2
? 2 ? = 100 ∫ ?? 2 ??
For the integral, let:
?=
?2
2
??
=?
??
? ?? =…
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