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5. Find the homogeneous differential equation whose general solution is y = 3 cos x - e3x/2 - 4x sin 2x.

5. Find the homogeneous differential equation whose general solution is y = 3 cos x - e3x/2 - 4x sin 2x.

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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Solve the problem and explain how the values of C1 - C7 were solved. 

5. Find the homogeneous differential equation whose general solution is y = 3 cos x - e3x/2 - 4x sin 2x.
Transcribed Image Text:5. Find the homogeneous differential equation whose general solution is y = 3 cos x - e3x/2 - 4x sin 2x.
HDE: +у= 3 соях ↓ (m²+i) (2m-3) (m³²+4)² = 0 m² = ADE (1²+1) (2D-3) (D²³+4) ³y = 0 moti M = ²/2 (31 (2x) - (4x) sin (2x) ax m= otai (2x) m=±15 - 4 (c₁ corbx + C₂ six) P=0 b= m = otu (m)² = (± √-T)² m² = -1 m² + 4 = 0 (2x) m² + 1 = 0) [C6=0 TC₁=-4 m = 23/1/2 2m=3 2m-3-0) y = [Gcosx + G₂s²x+c₂e³* + [Cucos2x) + CSS² 2x] [Cycos2x) + C₂ S 2x + x (Cocos ax G=3 C₂=0C3=-1 C4=0 C5=0 + Casax)
Transcribed Image Text:HDE: +у= 3 соях ↓ (m²+i) (2m-3) (m³²+4)² = 0 m² = ADE (1²+1) (2D-3) (D²³+4) ³y = 0 moti M = ²/2 (31 (2x) - (4x) sin (2x) ax m= otai (2x) m=±15 - 4 (c₁ corbx + C₂ six) P=0 b= m = otu (m)² = (± √-T)² m² = -1 m² + 4 = 0 (2x) m² + 1 = 0) [C6=0 TC₁=-4 m = 23/1/2 2m=3 2m-3-0) y = [Gcosx + G₂s²x+c₂e³* + [Cucos2x) + CSS² 2x] [Cycos2x) + C₂ S 2x + x (Cocos ax G=3 C₂=0C3=-1 C4=0 C5=0 + Casax)
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