{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:47:05Z","timestamp":1764859625051,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Integral transform methods are a common tool employed to study the Hyers\u2013Ulam stability of differential equations, including Laplace, Kamal, Tarig, Aboodh, Mahgoub, Sawi, Fourier, Shehu, and Elzaki integral transforms. This work provides improved techniques for integral transforms in relation to establishing the Hyers\u2013Ulam stability of differential equations with constant coefficients, utilizing the Kamal transform, where we focus on first- and second-order linear equations. In particular, in this work, we employ the Kamal transform to determine the Hyers\u2013Ulam stability and Hyers\u2013Ulam stability constants for first-order complex constant coefficient differential equations and, for second-order real constant coefficient differential equations, improving previous results obtained by using the Kamal transform. In a section of examples, we compare and contrast our results favorably with those established in the literature using means other than the Kamal transform.<\/jats:p>","DOI":"10.3390\/sym16020135","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T04:17:40Z","timestamp":1705983460000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Integral Transforms and the Hyers\u2013Ulam Stability of Linear Differential Equations with Constant Coefficients"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3069-2816","authenticated-orcid":false,"given":"Douglas R.","family":"Anderson","sequence":"first","affiliation":[{"name":"Department of Mathematics, Concordia College, Moorhead, MN 56562, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.jmaa.2013.02.034","article-title":"Laplace transform and Hyers\u2013Ulam stability of linear differential equations","volume":"403","author":"Rezaei","year":"2013","journal-title":"J. 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