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இந்த தேவதர்ஷினி சேத்தன்?இவரின் பின்னணி என்ன? Devadarshini was born in a Telugu speaking family in Chennai. 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#Bernoulli Bernoulli denklemleri nedir? Nasıl çözülür? İçerik: 0:00 Bernoulli denklemi nedir?","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4078716/0ac20da508b47bdda3e8b7c5cc67cb0e/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/zsw9lwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=videoid:4272172552936118662","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik eğitim içeriğidir. Eğitmen, Bernoulli diferansiyel denklemlerinin çözüm yöntemini detaylı şekilde anlatmaktadır.","Video, Bernoulli diferansiyel denklemlerinin genel formunu açıklayarak başlıyor ve bu denklemlerin lineer denklemlere nasıl dönüştürüleceğini beş basit adımda gösteriyor. Eğitmen önce teorik bilgileri veriyor, ardından örnek problemler üzerinden çözüm yöntemini adım adım gösteriyor. İlk örnek, Bernoulli denkleminin lineer denkleme dönüştürülmesi ve integral çarpanı yöntemiyle çözümü, ikinci örnek ise başlangıç değer problemi çözümüdür.","Videoda ayrıca integral çarpanı hesaplanması, genel çözümün bulunması ve başlangıç değer problemi çözümü gibi konular da ele alınmaktadır. Eğitmen, Bernoulli diferansiyel denklemlerinin çözümünün aslında çok zor olmadığını vurgulayarak videoyu sonlandırmaktadır."]},"endTime":664,"title":"Bernoulli Diferansiyel Denklemleri Çözüm Yöntemi","beginTime":0}],"fullResult":[{"index":0,"title":"Bernoulli Diferansiyel Denklemi","list":{"type":"unordered","items":["Bernoulli diferansiyel denklemi dy/dx + p(x)y + q(x)y^n formuna sahip birinci mertebeden diferansiyel denklemlerdir.","Bernoulli denkleminde n herhangi bir reel sayı olabilir; n=0 veya 1 ise denklem otomatikman lineer olur, n≠0 ise non-lineer olur.","Bernoulli diferansiyel denklemini çözmek için v=y^(1-n) dönüşümü kullanılır."]},"beginTime":0,"endTime":60,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=0&ask_summarization=1"},{"index":1,"title":"Bernoulli Denkleminin Lineer Hale Dönüştürülmesi","list":{"type":"unordered","items":["Bernoulli denkleminin lineer bir denkleme dönüştürülmesi beş basit adımda yapılır.","İlk adımda tüm terimler y^n'e bölünerek q yalnız bırakılır, ikinci adımda p'nin yanında oluşan y^(1-n) terimi dönüşüm fonksiyonu olarak alınır.","Üçüncü adımda dy/dx, v'nin türevi cinsinden hesaplanır ve dördüncü adımda dönüşüm gerçekleştirilir."]},"beginTime":60,"endTime":178,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=60&ask_summarization=1"},{"index":2,"title":"Lineer Denklemin Çözümü","list":{"type":"unordered","items":["Son adımda lineer denklem standart formunda yazılır, yani birinci türevin katsayısı 1 olacak şekilde tüm terimler 1-n ile çarpılır.","Standart formda elde edilen denklem integral çarpanı metodu kullanılarak çözülebilir.","Formül ezberlemeye gerek yoktur, beş basit adımı takip ederek Bernoulli diferansiyel denklemlerini kolaylıkla lineer denklemlere dönüştürebilirsiniz."]},"beginTime":178,"endTime":223,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=178&ask_summarization=1"},{"index":3,"title":"Örnek 1 - Bernoulli Denkleminin Çözümü","list":{"type":"unordered","items":["Örnek 1'de x dy/dx + y = 1/y^2 denklemi çözülmüştür.","Denklemin genel formunda yazılması için tüm terimler x'e bölünmüştür.","Dönüşüm v=y^3 kullanılarak denklem v'ye göre lineer hale getirilmiş ve integral çarpanı metoduyla çözülmüştür."]},"beginTime":223,"endTime":428,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=223&ask_summarization=1"},{"index":4,"title":"Örnek 2 - Başlangıç Değer Problemi","list":{"type":"unordered","items":["Örnek 2'de y^(1/2)y' + y^3 = 2 ve y(0) = 4 olacak şekilde bir başlangıç değer problemi verilmiştir.","Başlangıç değer 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eşittir."]},"beginTime":464,"endTime":497,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=464&ask_summarization=1"},{"index":6,"title":"Denklemin Çözümü İçin Dönüşüm","list":{"type":"unordered","items":["Denklemi çözmek için tüm terimler y üzeri eksi bir bölü iki'ye bölünür ve v = y üzeri üç iki dönüşümü yapılır.","y'nin türevi v'nin türevi olarak hesaplanır ve denklemde y üzeri üç iki yerine v ve v'nin türevi yazılır.","Sonuç olarak 3/2 v'nin türevi + v = 1 şeklinde lineer bir denklem elde edilir."]},"beginTime":497,"endTime":542,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=497&ask_summarization=1"},{"index":7,"title":"Lineer Denklemin Çözümü","list":{"type":"unordered","items":["Lineer denklemin standart formunda olması için v'nin türevinin katsayısı bir yapılır ve denklem 3/2 ile çarpılır.","Denklemin integral çarpanı e üzeri 3x/2 olarak hesaplanır ve integral çarpanı ile denklemin her iki tarafı çarpılır.","Her iki tarafta integral alınarak v = (1 + c × e üzeri -3x/2) / (2 × e üzeri -3x/2) şeklinde genel çözüm bulunur."]},"beginTime":542,"endTime":610,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=542&ask_summarization=1"},{"index":8,"title":"Başlangıç Değer Probleminin Çözümü","list":{"type":"unordered","items":["Başlangıç değer problemi için y(4) = 4 şartı kullanılarak c = 7 bulunur.","Aranan başlangıç değer probleminin çözümü y üzeri üç iki = (1 + 7 × e üzeri -3x/2) / (2 × e üzeri -3x/2) olur.","Bernoulli diferansiyel denklemleri, uygun dönüşümle lineer diferansiyel denkleme dönüştürülerek çözülebilir."]},"beginTime":610,"endTime":659,"href":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=610&ask_summarization=1"}],"linkTemplate":"/video/preview/4272172552936118662?parent-reqid=1769698268922709-8429246016837261758-balancer-l7leveler-kubr-yp-vla-239-BAL&text=Devadarshini+12+dd&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"12) Bernoulli Diferansiyel Denklemi (DD 12)","related_orig_text":"Devadarshini 12 dd","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Devadarshini 12 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