Verify that the following functions are indeed solutions to their respective ODEs (or IVPS). (a) Problem: y" + ²y = 0, Solution: y(x) = a cos(x) + b sin(x), where a, b are arbitrary constants. (b) Problem: y' = 0.5y, y(2) = 2,
Verify that the following functions are indeed solutions to their respective ODEs (or IVPS). (a) Problem: y" + ²y = 0, Solution: y(x) = a cos(x) + b sin(x), where a, b are arbitrary constants. (b) Problem: y' = 0.5y, y(2) = 2,
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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For questions a and b I have finished answers but feel uneasy about them could I receive a detailed answer for both parts a and b to understand them more thoroughly.
![Verify that the following functions are indeed solutions to their respective ODEs (or IVPs).
(a) Problem: y" + ²y = 0,
Solution: y(x) = a cos(πx) + b sin(x), where a, b are arbitrary constants.
(b) Problem: y' = 0.5y, y(2) = 2,
Solution: y(x)
initial condition.
=
ce0.5, where c is some constant you will need to determine as to satisfy the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6e52c04-e2c3-4e2d-83a7-f5740c8e0fd5%2F76cb8192-be7d-4118-9d2c-ae983e5c6726%2Fl6bdrfc_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the following functions are indeed solutions to their respective ODEs (or IVPs).
(a) Problem: y" + ²y = 0,
Solution: y(x) = a cos(πx) + b sin(x), where a, b are arbitrary constants.
(b) Problem: y' = 0.5y, y(2) = 2,
Solution: y(x)
initial condition.
=
ce0.5, where c is some constant you will need to determine as to satisfy the
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