Solve these recurrence relations together with the initial conditions given. Arrange the steps to solve the recurrence relation an = an - 2 for n ≥ 2 together with the initial conditions a = 5 and a1 = -1 in the correct order. Rank the options below. +α2 5=α1+ -1=-α1 + α2 2 − 1 = 0; r = −1, 1 an = α1(−1)" + α21” = α1(−1)^ + α2 α13 and a2 = 2 Therefore, an = 3 ⋅(-1)+2. ་ ་ Solve these recurrence relations together with the initial conditions given. Match the steps (in the right column) to their corresponding step numbers (in the left column) to solve the recurrence relation an=-6an-1-9an - 2 for n ≥ 2 together with the initial conditions a0 = 3 and a₁ = −3. Step 4 2 Step 3 3 Step 1 4 Step 2 Match each of the options above to the items below. The characteristic equation and its roots are 12 + 6r+ 9 = 0 and r = −3, −3, respectively. The general solution is an = α₁(-3)" + α2n(-3)". Using initial conditions, 3 = α1 and −3 = −3α1 – 302 After solving, α1 = 3 and a2 = −2. Therefore, an = 3. (-3)" -2n(-3)" = (3 - 2n)(-3)".

Solve these recurrence relations together with the initial conditions given. Arrange the steps to solve the recurrence relation an = an - 2 for n ≥ 2 together with the initial conditions a = 5 and a1 = -1 in the correct order. Rank the options below. +α2 5=α1+ -1=-α1 + α2 2 − 1 = 0; r = −1, 1 an = α1(−1)" + α21” = α1(−1)^ + α2 α13 and a2 = 2 Therefore, an = 3 ⋅(-1)+2. ་ ་ Solve these recurrence relations together with the initial conditions given. Match the steps (in the right column) to their corresponding step numbers (in the left column) to solve the recurrence relation an=-6an-1-9an - 2 for n ≥ 2 together with the initial conditions a0 = 3 and a₁ = −3. Step 4 2 Step 3 3 Step 1 4 Step 2 Match each of the options above to the items below. The characteristic equation and its roots are 12 + 6r+ 9 = 0 and r = −3, −3, respectively. The general solution is an = α₁(-3)" + α2n(-3)". Using initial conditions, 3 = α1 and −3 = −3α1 – 302 After solving, α1 = 3 and a2 = −2. Therefore, an = 3. (-3)" -2n(-3)" = (3 - 2n)(-3)".

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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