5. Which of the following is the expression for y₁? A. y₁ = ao (1-3x + x² – 2x³) 3 27 3 B. y₁ = a₁ (1 - ²x + ²x²5x³) o 16 C. y₁ = a₁ ao D. y₁ = ao (1-x+x²) (1-3x+x²) 6. Which of the following is the expression for y₁? (-1)^(n+2)x"] 4-3-3 A. y = ag x3 + Es B. y₂ = a3 [x³ + Σn=5 C. y2 = 04 [x¹ + 5 D. y₂ = a₁ [x+ + 5 (-1)"n(n+1)x"] 2.3n-3 (-1)"(n+1)x"] 5-32-4 (−1)"(n+1)(n+2)x"] 2-3-4 Obtain a solution to the following differential equation valid near the origin: x(x + 3)y" -9y' - 6y = 0 1. For the given differential equation, x = 0 is a/an: A. Regular point B. Ordinary point C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? A. y = Σ=1 anx"-" 100 B. y = Σ=0 anxn+r C. y = Σn=0 anx" D.y = n=1 anx" 3. The indicial equation for the given differential equation is: A. r(r - 4) = 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable 4. Using the suggested approach, the recurrence relation for n ≥ 1 is: A. 3(n + 4)(n-1)an-1 + n(n+4)an = 0 B. 3(n-4)(n+1)an−1 + n(n+1)an = 0 C. (n + 4)(n+1)an-1 + 3n(n + 4)an = 0 D. (n-4)(n+1)an-1 + 3n(n −4)an = 0

5. Which of the following is the expression for y₁? A. y₁ = ao (1-3x + x² – 2x³) 3 27 3 B. y₁ = a₁ (1 - ²x + ²x²5x³) o 16 C. y₁ = a₁ ao D. y₁ = ao (1-x+x²) (1-3x+x²) 6. Which of the following is the expression for y₁? (-1)^(n+2)x"] 4-3-3 A. y = ag x3 + Es B. y₂ = a3 [x³ + Σn=5 C. y2 = 04 [x¹ + 5 D. y₂ = a₁ [x+ + 5 (-1)"n(n+1)x"] 2.3n-3 (-1)"(n+1)x"] 5-32-4 (−1)"(n+1)(n+2)x"] 2-3-4 Obtain a solution to the following differential equation valid near the origin: x(x + 3)y" -9y' - 6y = 0 1. For the given differential equation, x = 0 is a/an: A. Regular point B. Ordinary point C. Regular singular point D. Irregular singular point 2. Which of the following is the correct form for the solution y? A. y = Σ=1 anx"-" 100 B. y = Σ=0 anxn+r C. y = Σn=0 anx" D.y = n=1 anx" 3. The indicial equation for the given differential equation is: A. r(r - 4) = 0 B. r(2r + 1) = 0 C. r(r-3) = 0 D. None of these/Not applicable 4. Using the suggested approach, the recurrence relation for n ≥ 1 is: A. 3(n + 4)(n-1)an-1 + n(n+4)an = 0 B. 3(n-4)(n+1)an−1 + n(n+1)an = 0 C. (n + 4)(n+1)an-1 + 3n(n + 4)an = 0 D. (n-4)(n+1)an-1 + 3n(n −4)an = 0

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 15E: Use Eulers method to approximate the indicated function value to 3 decimal places, using h=0.1....

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