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Determining a Solution In Exercises 15-22, determine whether the function is a solution of the differential equation y(4) 16y = 0. 21. y = ln x + e²x + Cx4 -

Determining a Solution In Exercises 15-22, determine whether the function is a solution of the differential equation y(4) 16y = 0. 21. y = ln x + e²x + Cx4 -

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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**Determining a Solution** In Exercises 15–22, determine whether the function is a solution of the differential equation \( y^{(4)} - 16y = 0 \). 21. \( y = \ln x + e^{2x} + Cx^4 \) --- **Explanation:** The task is to verify if the given function \( y = \ln x + e^{2x} + Cx^4 \) satisfies the fourth-order linear differential equation \( y^{(4)} - 16y = 0 \). This involves calculating the fourth derivative of the function, substituting it into the equation, and checking if it yields zero.
Transcribed Image Text:**Determining a Solution** In Exercises 15–22, determine whether the function is a solution of the differential equation \( y^{(4)} - 16y = 0 \). 21. \( y = \ln x + e^{2x} + Cx^4 \) --- **Explanation:** The task is to verify if the given function \( y = \ln x + e^{2x} + Cx^4 \) satisfies the fourth-order linear differential equation \( y^{(4)} - 16y = 0 \). This involves calculating the fourth derivative of the function, substituting it into the equation, and checking if it yields zero.
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