{"id":2259,"date":"2022-02-24T18:25:28","date_gmt":"2022-02-24T09:25:28","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2259"},"modified":"2025-05-05T12:37:53","modified_gmt":"2025-05-05T03:37:53","slug":"%e6%9c%80%e3%82%82%e7%b0%a1%e5%8d%98%e3%81%aa%e5%ae%9a%e6%95%b0%e4%bf%82%e6%95%b02%e9%9a%8e%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/%e6%9c%80%e3%82%82%e7%b0%a1%e5%8d%98%e3%81%aa%e5%ae%9a%e6%95%b0%e4%bf%82%e6%95%b02%e9%9a%8e%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/","title":{"rendered":"\u6700\u3082\u7c21\u5358\u306a\u5b9a\u6570\u4fc2\u65702\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f"},"content":{"rendered":"

\u6700\u3082\u7c21\u5358\u306a\u5b9a\u6570\u4fc2\u65702\u968e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f \\(y^{”} + y = 0\\) \u3068 \\(y^{”} -y = 0\\) \u3092\u89e3\u304f\u3002<\/p>\n

\\(y^{”} + y = 0\\)<\/h3>\n

\u89e3\u304f\u3079\u304d\u5fae\u5206\u65b9\u7a0b\u5f0f \\(y^{”} + y = 0\\) \u3092\u3061\u3087\u3063\u3068\u79fb\u9805\u3057\u3066\u3084\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3044\u3046\u3053\u3068\u306b\u3059\u308b\u3002$$ y^{”} = -y$$<\/p>\n

\u672a\u77e5\u95a2\u6570 \\(y(x)\\) \u304c\u3042\u308b\u3002\u3053\u306e \\(y\\) \u3092 \\(x\\) \u30672\u968e\u5fae\u5206\u3059\u308b\u3068\uff0c\u81ea\u5206\u81ea\u8eab\u306b\u30de\u30a4\u30ca\u30b9\u306e\u7b26\u53f7\u304c\u3064\u304f \\(-y\\) \u306b\u306a\u3063\u305f\u3002\u3055\u3066 \\(y\\) \u306f\u4f55\u3067\u3057\u3087\u3046\uff1f\u3068\u3044\u3046\u554f\u984c\u3002<\/p>\n

\u3053\u308c\u307e\u3067\u306e\u4eba\u751f\u306e\u306a\u304b\u3067\u7686\u3055\u3093\u304c\u84c4\u3048\u305f\u5168\u3066\u306e\u95a2\u6570\u306e\u77e5\u8b58\u304b\u3089\uff0c2\u968e\u5fae\u5206\u3057\u305f\u3089\u81ea\u5206\u81ea\u8eab\u306b\u30de\u30a4\u30ca\u30b9\u304c\u3064\u3044\u305f\u3082\u306e\u306b\u306a\u308b\u95a2\u6570\u3092\u63a2\u3057\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n

\u3059\u308b\u3068… \uff08\u53c2\u8003\uff1a2\u968e\u5fae\u5206\u3059\u308b\u3068\u81ea\u5206\u81ea\u8eab\u306b\u30de\u30a4\u30ca\u30b9\u304c\u3064\u304f\u95a2\u6570<\/a>\uff09<\/p>\n

\\( y_1 = \\cos x\\) \u3068\uff0c\\(y_2 = \\sin x\\) \u304c\u898b\u3064\u304b\u308b\uff01\uff08\u30cf\u30ba\uff09<\/p>\n

\u5b9f\u969b\u306b\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\uff0c<\/p>\n

$$y’_1 = -\\sin x, \\quad y^{”}_1 = -\\cos x = -y_1$$<\/p>\n

\u78ba\u304b\u306b\u306a\u3063\u3066\u3044\u308b\u3002\\(y_2\\) \u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u78ba\u304b\u3081\u3089\u308c\u308b\u3002<\/p>\n

\u306a\u306e\u3067\uff0c\u4eca\u5f8c\u306f \\( y^{”} = -y \\)\u00a0 \u3068\u3044\u3046\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u307f\u305f\u3089\uff0c\u810a\u9ac4\u53cd\u5c04\u3067<\/strong><\/span><\/p>\n

\u300c2\u3064\u306e\u89e3\u306f \\(\\cos x\\) \u3068\\(\\sin x\\) \u3060\u30fc\u3063\uff01<\/strong><\/span>\u300d<\/p>\n

\u3068\u53eb\u3093\u3067\u304f\u3060\u3055\u3044\u3002<\/p>\n

 <\/p>\n

\u3053\u306e\u3088\u3046\u306b\uff0c2\u968e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e1\u6b21\u72ec\u7acb\u306a\u89e3<\/strong><\/u><\/span>\u306f2\u3064\u3002\u4e00\u822c\u89e3\u306f\u3053\u308c\u3089\u306e\u7dda\u5f62\u548c\u3067\u66f8\u3051\u308b\u306e\u3067\uff0c\u4efb\u610f\u5b9a\u6570 \\(C_1, C_2\\) \uff08\u3053\u308c\u304c2\u3064\u306e\u7a4d\u5206\u5b9a\u6570\u306b\u306a\u308b\uff09\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n

$$ y(x) = C_1 \\, y_1 + C_2\\, y_2 = C_1\\, \\cos x + C_2 \\, \\sin x$$<\/p>\n

2\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u306f\u4e00\u822c\u306b\u7a4d\u5206\u5b9a\u6570\u304c2\u3064\u3002\u305d\u308c\u304c\u3053\u308c\u3089 \\(C_1, \\, C_2\\)\u3002<\/p>\n

 <\/p>\n

\\(y^{”}\u00a0 -y = 0\\)<\/h3>\n

\u89e3\u304f\u3079\u304d\u5fae\u5206\u65b9\u7a0b\u5f0f \\(y^{”}\u00a0 -y = 0\\) \u3092\u3061\u3087\u3063\u3068\u79fb\u9805\u3057\u3066\u3084\u3063\u3066\uff0c\u4ee5\u4e0b\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3044\u3046\u3053\u3068\u306b\u3059\u308b\u3002$$ y^{”} = y$$<\/p>\n

\u672a\u77e5\u95a2\u6570 \\(y(x)\\) \u304c\u3042\u308b\u3002\u3053\u306e \\(y\\) \u3092 \\(x\\) \u30672\u968e\u5fae\u5206\u3059\u308b\u3068\uff0c\u81ea\u5206\u81ea\u8eab\u306b\u306a\u3063\u305f\u3002\u3055\u3066\\(y\\) \u306f\u4f55\u3067\u3057\u3087\u3046\uff1f\u3068\u3044\u3046\u554f\u984c\u3002<\/p>\n

\u3053\u308c\u307e\u3067\u306e\u4eba\u751f\u306e\u306a\u304b\u3067\u7686\u3055\u3093\u304c\u84c4\u3048\u305f\u5168\u3066\u306e\u95a2\u6570\u306e\u77e5\u8b58\u304b\u3089\uff0c2\u968e\u5fae\u5206\u3057\u305f\u3089\u81ea\u5206\u81ea\u8eab\u306b\u306a\u308b\u95a2\u6570\u3092\u63a2\u3057\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n

\u3059\u308b\u3068… \uff08\u53c2\u8003\uff1a2\u968e\u5fae\u5206\u3059\u308b\u3068\u81ea\u5206\u81ea\u8eab\u306b\u306a\u308b\u95a2\u6570<\/a>\uff09<\/p>\n

\u53cc\u66f2\u7dda\u95a2\u6570 \\(\\cosh x\\) \u3068 \\(\\sinh x\\) \uff08\u3042\u308b\u3044\u306f\uff0c\\( y_1 = e^x\\) \u3068\uff0c\\(y_2 = e^{-x}\\)\uff09\u304c\u898b\u3064\u304b\u308b\uff01\uff08\u30cf\u30ba\uff09<\/p>\n

\u306a\u306e\u3067\uff0c\u4eca\u5f8c\u306f \\( y^{”} =\u00a0 y \\)\u00a0 \u3068\u3044\u3046\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u307f\u305f\u3089\uff0c\u810a\u9ac4\u53cd\u5c04\u3067<\/strong><\/span><\/p>\n

\u300c2\u3064\u306e\u89e3\u306f \\(\\cosh x\\) \u3068\\(\\sinh x\\) \u3060\u30fc\u3063\uff01<\/strong><\/span>\u300d<\/p>\n

\u3068\u53eb\u3093\u3067\u304f\u3060\u3055\u3044\u3002<\/p>\n

\u3042\u308b\u3044\u306f\uff0c\u810a\u9ac4\u53cd\u5c04\u3067<\/strong><\/span><\/p>\n

\u300c2\u3064\u306e\u89e3\u306f \\(e^x\\) \u3068\\(e^{-x}\\) \u3060\u30fc\u3063\uff01<\/strong><\/span>\u300d<\/p>\n

\u3068\u53eb\u3093\u3067\u3082\u3088\u308d\u3057\u3044\u3067\u3059\u3002<\/p>\n

 <\/p>\n

\u3053\u306e\u3088\u3046\u306b\uff0c2\u968e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e1\u6b21\u72ec\u7acb\u306a\u89e3<\/strong><\/u><\/span>\u306f2\u3064\u3002\u4e00\u822c\u89e3\u306f\u3053\u308c\u3089\u306e\u7dda\u5f62\u548c\u3067\u66f8\u3051\u308b\u306e\u3067\uff0c\u4efb\u610f\u5b9a\u6570 \\(C_1, C_2\\) \uff08\u3053\u308c\u304c2\u3064\u306e\u7a4d\u5206\u5b9a\u6570\u306b\u306a\u308b\uff09\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n

$$y(x) = C_1 \\, y_1 + C_2\\, y_2 = C_1 \\cosh x + C_2 \\sinh x$$<\/p>\n

\u3042\u308b\u3044\u306f<\/p>\n

$$ y(x) = C_1 \\, y_1 + C_2\\, y_2 = C_1\\, e^x + C_2 \\, e^{-x}$$<\/p>\n

\\(y^{”}\u00a0 = 0\\)<\/h3>\n

2\u968e\u5fae\u5206\u3057\u3066\u30bc\u30ed\u3068\u3044\u3046\u3053\u3068\u306f\uff0c\u305f\u304b\u3060\u304b $x$ \u306e1\u6b21\u307e\u3067\u306e\u95a2\u6570\u3060\u3068\u3044\u3046\u3053\u3068\u3060\u304b\u3089<\/p>\n

$$y = A + B x$$<\/p>\n","protected":false},"excerpt":{"rendered":"

\u6700\u3082\u7c21\u5358\u306a\u5b9a\u6570\u4fc2\u65702\u968e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f \\(y^{”} + y = 0\\) \u3068 \\(y^{”} -y = 0\\) \u3092\u89e3\u304f\u3002<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":2224,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2259","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2259"}],"version-history":[{"count":14,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2259\/revisions"}],"predecessor-version":[{"id":10220,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2259\/revisions\/10220"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2224"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}