A liters 45 a p t 1000 e sin 2 t b p t

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Unformatted text preview: = 32 (1 − e−kt ) k (b) 1 − e−kt < 1; e−kt → 0 as t → ∞ 39. (a) i(t ) = E [1 − e−(R/L)t ] R E (b) i(t ) → (amps) as t → ∞ R L (c) t = ln 10 seconds R 43. (a) liters 45. (a) P (t ) = 1000 e( sin 2π t )/π (b) P (t ) = 2000 e( sin 2π t )/π − 1000 SECTION 8.9 1. y = C e−(1/2) cos (2x+3) 9. ln | y + 1| + 3. x4 + 2 =C y2 5. y sin y + cos y = − cos 1 x +C √ 7. e−y = ex − xex + C 1 − x2 15. y + ln | y| = x3 −x−5 3 1 = ln | ln x| + C y+1 11. y2 = C ( ln x)2 − 1 13. sin−1 y = 1 − ANSWERS TO ODD-NUMBERED EXERCISES 17. x2 1 + x + ln ( y2 + 1) − tan−1 y = 4 2 2 19. y = ln 3e2x − 2 23. x2 − y2 = C y y= x y 3 2 A-65 21. y = 3 x + C 2 25. y2 = −2x + C y x2 – y 2 = 1 y 2 = –2 x y = ex xy = 1 1 x xy = –1 x x y=– 2 3 y 2 – x2 = 1 x 27. A differential equation for the given family is y2 = 2xyy + y2 (y )2 . Now replace y by − which simplifies to y2 = 2xyy + y2 ( y )2 . Thus the given family is self-orthogonal. 29. (a) C (t ) = 31. (a) v(t ) = 33. (a) y(t ) = kA2 t 0 1 + kA0 t α c e(α/m)t −β (b) C (t...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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