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y"" - √xy = sinx; y(π) = 0, y' (π) = 11, y" (π) = 3

y"" - √xy = sinx; y(π) = 0, y' (π) = 11, y" (π) = 3

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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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: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 \( x = \pi \).
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.
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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