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विकलक समीकरणाची पदवी  आहे

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  1. 3
  2. 1
  3. 2
  4. 6

Answer (Detailed Solution Below)

Option 2 : 1

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स्पष्टीकरण:

विकलक समीकरणाची पदवी:

  • विकलक समीकरणाची पदवी दिलेल्या विकलक समीकरणातील सर्वोच्च क्रम व्यूत्पन्नाच्या सामर्थ्याने दर्शवली जाते.
  • पदवी परिभाषित करण्यासाठी विकलक समीकरण डेरीव्हेटीव्हज मधील बहुपदी असणे आवश्यक आहे.

उदाहरण: 

  • येथे सर्वोच्च क्रम व्यूत्पन्नाचा घातांक एक आहे (म्हणजे द्वितीय क्रम) आणि दिलेले विकलक समीकरण व्यूत्पन्नामध्ये बहुपदी समीकरण आहे.म्हणून या समीकरणाची डिग्री 1 आहे.

उदाहरण: 

  • या समीकरणाचा क्रम 3 आहे आणि पदवी 2 आहे कारण सर्वोच्च व्यूत्पन्न 2 आहे.

विकलक समीकरणाचा क्रम:

  • विकलक समीकरणे ऑर्डरच्या आधारावर वर्गीकृत केली जातात.
  • विकलक समीकरणाचा क्रम हा समीकरणामध्ये उपस्थित असलेल्या सर्वोच्च व्यूत्पन्न (याला विकलक विभाजक असेही म्हणतात) क्रम असतो.

उदाहरण: 

  • या समीकरणामध्ये, सर्वोच व्यूत्पन्नाचा क्रम 4 आहे म्हणून हे चौथ्या क्रमाचे विकलक समीकरण आहे.

उदाहरण: 

  • हे समीकरण थर्ड-ऑर्डर विकलक समीकरण दर्शवते. 
  • अशाप्रकारे आपल्याकडे उच्च-क्रम भिन्न समीकरणे असू शकतात, म्हणजे nth

 क्रम भिन्न  समीकरणे.

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