Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. ²8 +16y=0; y=c₁e4x + ₂x4x d²y dx² dx When y = c₁e4x + c2xe4x
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. ²8 +16y=0; y=c₁e4x + ₂x4x d²y dx² dx When y = c₁e4x + c2xe4x
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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I'm having difficulty with my second derivative, I feel like I am missing a detail and it is messing me up!
![Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d²y - gdy + 16y = 0;
dx²
dx
When y = c₁e4x + ₂xe4x,
dy
dx
y = c₁e¹x + ₂x4x
4x
40₁ · 0²¹² + ((0₂ · 6¹x) + (0₂x-4e¹4x))
∙e
B²y = (0₁·160¹x) + (0₂-404x) + [(x-40²4x) + (0₂-x-160¹x)]
•4e
dx²
Thus, in terms of x,
²-8dx + 16 =
+ 16(c₁e4x + c₂xe4x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76aaab3c-5a4a-4ff8-814d-d2e8a1f30217%2F75180eb7-4e64-4338-ac46-b334213c8595%2Fiakjplq_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d²y - gdy + 16y = 0;
dx²
dx
When y = c₁e4x + ₂xe4x,
dy
dx
y = c₁e¹x + ₂x4x
4x
40₁ · 0²¹² + ((0₂ · 6¹x) + (0₂x-4e¹4x))
∙e
B²y = (0₁·160¹x) + (0₂-404x) + [(x-40²4x) + (0₂-x-160¹x)]
•4e
dx²
Thus, in terms of x,
²-8dx + 16 =
+ 16(c₁e4x + c₂xe4x)
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