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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Solve the problem and explain how the values of C1 - C7 were solved.
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26f20fad-e544-4d30-9da3-66767dad5e52%2F9fb6467e-45cb-4859-bca9-70ad59eb2fd2%2Fbcqzc0w_processed.png&w=3840&q=75)
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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