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Find the general solution of the following equation: y" – 2y + 4y = 0. O yG (x) = c1e* cos(x) + c2e* sin(x) O yG (x) = c1e* cos (V3x) + c2e* sin(v3x) O yG (x) = c1e* + c2xe* O yG (x) = c1 cos(/3x) + c2 sin(v3x) O yG (x) = c1ev3x cos(x) + c2ev3x sin(x)

Find the general solution of the following equation: y" – 2y + 4y = 0. O yG (x) = c1e* cos(x) + c2e* sin(x) O yG (x) = c1e* cos (V3x) + c2e* sin(v3x) O yG (x) = c1e* + c2xe* O yG (x) = c1 cos(/3x) + c2 sin(v3x) O yG (x) = c1ev3x cos(x) + c2ev3x sin(x)

Advanced Engineering Mathematics
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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Find the general solution of the following equation: \[ y'' - 2y' + 4y = 0. \] Options: 1. \( y_G(x) = c_1 e^x \cos(x) + c_2 e^x \sin(x) \) 2. \( y_G(x) = c_1 e^x \cos(\sqrt{3}x) + c_2 e^x \sin(\sqrt{3}x) \) 3. \( y_G(x) = c_1 e^x + c_2 x e^x \) 4. \( y_G(x) = c_1 \cos(\sqrt{3}x) + c_2 \sin(\sqrt{3}x) \) 5. \( y_G(x) = c_1 e^{\sqrt{3}x} \cos(x) + c_2 e^{\sqrt{3}x} \sin(x) \)
Transcribed Image Text:Find the general solution of the following equation: \[ y'' - 2y' + 4y = 0. \] Options: 1. \( y_G(x) = c_1 e^x \cos(x) + c_2 e^x \sin(x) \) 2. \( y_G(x) = c_1 e^x \cos(\sqrt{3}x) + c_2 e^x \sin(\sqrt{3}x) \) 3. \( y_G(x) = c_1 e^x + c_2 x e^x \) 4. \( y_G(x) = c_1 \cos(\sqrt{3}x) + c_2 \sin(\sqrt{3}x) \) 5. \( y_G(x) = c_1 e^{\sqrt{3}x} \cos(x) + c_2 e^{\sqrt{3}x} \sin(x) \)
**Problem Statement:** Find the general solution of the following equation: \( y'' - 6y' + 7y = 0. \) **Answer Choices:** 1. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 e^{-3\sqrt{2}x} \) 2. \( y_G(x) = c_1 e^{(3+\sqrt{2})x} + c_2 e^{(3-\sqrt{2})x} \) 3. \( y_G(x) = c_1 e^{3x} + c_2 e^{-3x} \) 4. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 e^{-\sqrt{2}x} \) 5. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 x e^{-\sqrt{2}x} \)
Transcribed Image Text:**Problem Statement:** Find the general solution of the following equation: \( y'' - 6y' + 7y = 0. \) **Answer Choices:** 1. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 e^{-3\sqrt{2}x} \) 2. \( y_G(x) = c_1 e^{(3+\sqrt{2})x} + c_2 e^{(3-\sqrt{2})x} \) 3. \( y_G(x) = c_1 e^{3x} + c_2 e^{-3x} \) 4. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 e^{-\sqrt{2}x} \) 5. \( y_G(x) = c_1 e^{\sqrt{2}x} + c_2 x e^{-\sqrt{2}x} \)
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