y"" - √xy = sinx; y(π) = 0, y' (π) = 11, y" (π) = 3
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
![The image presents a differential equation and initial conditions, which appear as follows:
\[ y''' - \sqrt{x} y = \sin x; \]
Initial conditions:
\[ y(\pi) = 0, \quad y'(\pi) = 11, \quad y''(\pi) = 3 \]
Explanation:
This is a third-order differential equation involving the function \( y \) and its derivatives. The equation is:
- \( y''' \): The third derivative of \( y \) with respect to \( x \).
- \( \sqrt{x} y \): The product of the square root of \( x \) and the function \( y \).
- \(\sin x\): The sine function at \( x \).
The initial conditions specify the values of the function and its first and second derivatives at \( x = \pi \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7a11c6-35df-4daf-855c-043e8f69fb75%2F83d8624e-7371-413c-a4b7-4d0ebfe8b77c%2F4p8em2g_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a differential equation and initial conditions, which appear as follows:
\[ y''' - \sqrt{x} y = \sin x; \]
Initial conditions:
\[ y(\pi) = 0, \quad y'(\pi) = 11, \quad y''(\pi) = 3 \]
Explanation:
This is a third-order differential equation involving the function \( y \) and its derivatives. The equation is:
- \( y''' \): The third derivative of \( y \) with respect to \( x \).
- \( \sqrt{x} y \): The product of the square root of \( x \) and the function \( y \).
- \(\sin x\): The sine function at \( x \).
The initial conditions specify the values of the function and its first and second derivatives at \( x = \pi \).
Transcribed Image Text:In Problems 1–6, determine the largest interval \((a, b)\) for which Theorem 1 guarantees the existence of a unique solution on \((a, b)\) to the given initial value problem.
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