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REDUCTION OF ORDER AND VARIATION OF PARAMETERS 1. (D² + 4) y = tan 2x 2. (D² + 8D + 16)y = C. 1-e4x

REDUCTION OF ORDER AND VARIATION OF PARAMETERS 1. (D² + 4) y = tan 2x 2. (D² + 8D + 16)y = C. 1-e4x

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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D. EXPONENTIAL SHIFTING THEOREM 1. (D3 + 4D2 - 3D — 18)у %3D 24х3е 3х 2. (D² + 4D + 4)y = 64x²e¬* | Е. INVERSE D-OPERATOR 1. (D² + 3D + 2)y = 24cos3x 2. (D³ + 4D² + 5D)y = 20e¬5x 3. (D4 + 5D³ + 6D² – 4D – 8)y = 60e-5x 4. (D3 + 6D² + 13D)y = 36e-3x sin 2x
Transcribed Image Text:D. EXPONENTIAL SHIFTING THEOREM 1. (D3 + 4D2 - 3D — 18)у %3D 24х3е 3х 2. (D² + 4D + 4)y = 64x²e¬* | Е. INVERSE D-OPERATOR 1. (D² + 3D + 2)y = 24cos3x 2. (D³ + 4D² + 5D)y = 20e¬5x 3. (D4 + 5D³ + 6D² – 4D – 8)y = 60e-5x 4. (D3 + 6D² + 13D)y = 36e-3x sin 2x
HOMOGENEOUS HIGHER ORDERED LDE 1. (D5–12Dª + 520D3-112D² + 192D– 256)y = 0 2. (D5-7Dª-31D³ + 103D² + 150D- 216)y = 0 A. В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D³ + 5D² + 3D - 9)y 2. (D3 + 13D – 34)y = 25x2 + 100e*cos4x 64x?e-3x С. REDUCTION OF ORDER AND VARIATION OF PARAMETERS 1.(D? + 4) у %3 tan 2x 2. (D2 + 8D + 16)y = 1 1-e4x
Transcribed Image Text:HOMOGENEOUS HIGHER ORDERED LDE 1. (D5–12Dª + 520D3-112D² + 192D– 256)y = 0 2. (D5-7Dª-31D³ + 103D² + 150D- 216)y = 0 A. В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D³ + 5D² + 3D - 9)y 2. (D3 + 13D – 34)y = 25x2 + 100e*cos4x 64x?e-3x С. REDUCTION OF ORDER AND VARIATION OF PARAMETERS 1.(D? + 4) у %3 tan 2x 2. (D2 + 8D + 16)y = 1 1-e4x
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