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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.