1. Solve the initial value problem x'(t) = [11]x(t) + [] x(0) : -=[7]. - [8 Ste³+8e³-10e 4te³ +2e³ +5e 1 solution: x(t) 2. Find the general solutions of 4y" - y = solution: y(t) = -4+ 8e ¹/² In (2+ e¹/2) + te¹/² - 2e¹/² In (2 + e¹/²) + C₁e¹/² + C₂ ¹/² 3. Find the general solutions of x': 8e¹/2 2+e¹/2 2 3 -3 42-4x+ 43-5 solution: x(t) = te 2¹ 21 te Het 31 -21 14c² te-21 14e² e2 In(1+e¹) - e 2¹ In (1 + e²) + e²¹ In(1+e)+C₁e -e 2¹ In(1+e') + e²¹ In(1+e²), H A +C₂e 21 1+C3e²¹ H
1. Solve the initial value problem x'(t) = [11]x(t) + [] x(0) : -=[7]. - [8 Ste³+8e³-10e 4te³ +2e³ +5e 1 solution: x(t) 2. Find the general solutions of 4y" - y = solution: y(t) = -4+ 8e ¹/² In (2+ e¹/2) + te¹/² - 2e¹/² In (2 + e¹/²) + C₁e¹/² + C₂ ¹/² 3. Find the general solutions of x': 8e¹/2 2+e¹/2 2 3 -3 42-4x+ 43-5 solution: x(t) = te 2¹ 21 te Het 31 -21 14c² te-21 14e² e2 In(1+e¹) - e 2¹ In (1 + e²) + e²¹ In(1+e)+C₁e -e 2¹ In(1+e') + e²¹ In(1+e²), H A +C₂e 21 1+C3e²¹ H
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Solve the initial value problem x'(t) = [1₁₁]xt) +
solution: x(t) =
2. Find the general solutions of 4y" - y
[6],
[1]×0+ [6] - [7]
x(0) =
=
[Ste³t+8e³t 10e
4te³1 +2e³1 +5e ²
3. Find the general solutions of x' =
solution: y(t) = −4+ 8e ¹/² In (2 + e¹/2) + te¹/² - 2e¹/² In (2+ e¹/²) + C₁e¹/² + C₂ ¹/²
8e¹/2
2+¹/2
solution: x(t) =
2 3-3
4
4
2-4x+
3-5
te
te
Het
est te
14e²
²³1-21
Het
] +0€ + []+0₂= ²] + =]
H
21
e²¹ ln(1 + e¹)
21
¹ e 2¹ ln(1 + e¹) + e²¹ ln(1 + e') +C₁e ¹
- e 2¹ In(1+e¹) + e²¹ In(1+e²),
21](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c89c353-252e-4eca-b673-064be33ffdb0%2Fc529afb6-fea0-4430-9235-a3335de28fee%2Fv9sj3s_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the initial value problem x'(t) = [1₁₁]xt) +
solution: x(t) =
2. Find the general solutions of 4y" - y
[6],
[1]×0+ [6] - [7]
x(0) =
=
[Ste³t+8e³t 10e
4te³1 +2e³1 +5e ²
3. Find the general solutions of x' =
solution: y(t) = −4+ 8e ¹/² In (2 + e¹/2) + te¹/² - 2e¹/² In (2+ e¹/²) + C₁e¹/² + C₂ ¹/²
8e¹/2
2+¹/2
solution: x(t) =
2 3-3
4
4
2-4x+
3-5
te
te
Het
est te
14e²
²³1-21
Het
] +0€ + []+0₂= ²] + =]
H
21
e²¹ ln(1 + e¹)
21
¹ e 2¹ ln(1 + e¹) + e²¹ ln(1 + e') +C₁e ¹
- e 2¹ In(1+e¹) + e²¹ In(1+e²),
21
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