Misc 10 - Chapter 9 Class 12 Differential Equations (Important Question)

Last updated at April 16, 2024 by

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Misc 10 Solve the differential equation [š‘’^(āˆ’2āˆšš‘„)/āˆšš‘„āˆ’š‘¦/āˆšš‘„] š‘‘š‘„/š‘‘š‘¦=1(š‘„ā‰ 0)[š‘’^(āˆ’2āˆšš‘„)/āˆšš‘„āˆ’š‘¦/āˆšš‘„] š‘‘š‘„/š‘‘š‘¦=1 š‘’^(āˆ’2āˆšš‘„)/āˆšš‘„āˆ’ š‘¦/āˆšš‘„ =š‘‘š‘¦/š‘‘š‘„ š’…š’š/š’…š’™ + š’š/āˆšš’™ = š’†^(āˆ’šŸāˆšš’™)/āˆšš’™ Differential equation is of the form š‘‘š‘¦/š‘‘š‘„ + Py = Q where P = šŸ/āˆšš’™ & Q = š’†^(āˆ’šŸāˆšš’™)/āˆšš’™ IF. = eāˆ«1ā–’"pdx" Finding āˆ«1ā–’怖š‘· š’…š’™ć€— āˆ«1ā–’怖š‘· š’…š’™=āˆ«1ā–’š’…š’™/āˆšš’™ 怗 āˆ«1ā–’怖š‘ƒ š‘‘š‘„=āˆ«1ā–’怖š‘„^((āˆ’1)/2) š‘‘š‘„怗 怗 āˆ«1ā–’怖š‘ƒ š‘‘š‘„=āˆ«1ā–’怖(š‘„ (āˆ’1)/2 + 1)/((āˆ’1)/2 + 1) š‘‘š‘„怗 怗 āˆ«1ā–’怖š‘ƒ š‘‘š‘„=2š‘„^(1/2) 怗= 2āˆšš‘„ āˆ“ IF = š’†^(šŸāˆšš’™) Solution is y (IF) = āˆ«1ā–’怖(š‘„Ć—š¼š¹)š‘‘š‘„+š‘ć€— yš’†^(šŸāˆšš’™) = āˆ«1ā–’怖(š’†^(āˆ’šŸāˆšš’™)/āˆšš’™Ć—š’†^(šŸāˆšš’™) )š’…š’™+š’„怗 yš‘’^(2āˆšš‘„) = āˆ«1ā–’怖š‘‘š‘„/āˆšš‘„+š‘ć€— yš‘’^(2āˆšš‘„) = āˆ«1ā–’怖1/āˆšš‘„ š‘‘š‘„+š‘ć€— yš‘’^(2āˆšš‘„) = āˆ«1ā–’怖š‘„^((āˆ’1)/2) š‘‘š‘„+š‘ć€— yš‘’^(2āˆšš‘„) = āˆ«1ā–’怖(š‘„^(āˆ’1/2 + 1) )/(āˆ’1/2 + 1)+š‘ć€— "y" š‘’^(2āˆšš‘„) " = "2š‘„^(1/2) + C "y" š’†^(šŸāˆšš’™) " = "2āˆšš’™ + C

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.