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Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 10, 2026 by

Solve the differential equation: ye^(x/y) dx=(xe^(x/y)+y^2 )dy,(y≠0)

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This question is similar to Example 12 Chapter 9 Class 12

[Video] Solve differential equation y e^x/y dx = (x e^(x/y) + y^2) dy - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
part 3 - Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12 part 4 - Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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yš‘’^(š‘„/š‘¦) š‘‘š‘„=(š‘„š‘’^(š‘„/š‘¦)+š‘¦^2 )š‘‘š‘¦ Step 1: Finding š‘‘š‘„/š‘‘š‘¦ yš‘’^(š‘„/š‘¦) š‘‘š‘„=(š‘„š‘’^(š‘„/š‘¦)+š‘¦^2 )š‘‘š‘¦ š’…š’™/š’…š’š=(š’™š’†^(š’™/š’š) + š’š^šŸ)/(š’šš’†^(š’™/š’š) ) Step 2 : Solving š‘‘š‘„/š‘‘š‘¦ by Putting š‘„=š‘£š‘¦ š‘‘š‘„/š‘‘š‘¦=(š‘„š‘’^(š‘„/š‘¦) + š‘¦^2)/(š‘¦š‘’^(š‘„/š‘¦) ) Put š’™=š’—š’š Diff. w.r.t. š‘¦ š‘‘š‘„/š‘‘š‘¦=š‘‘/š‘‘š‘¦ (š‘£š‘¦) š‘‘š‘„/š‘‘š‘¦=š‘¦ . š‘‘š‘£/š‘‘š‘¦+š‘£ š‘‘š‘¦/š‘‘š‘¦ š’…š’™/š’…š’š=š’š . š’…š’—/š’…š’š+š’— Putting values of š‘‘š‘„/š‘‘š‘¦ and x in (1) š‘‘š‘„/š‘‘š‘¦=(š‘„š‘’^(š‘„/š‘¦)+š‘¦^2)/(š‘¦š‘’^(š‘„/š‘¦) ) š’—+š’š š’…š’—/š’…š’š=(š’—š’šš’†^š’—+š‘¦^2)/(š’šš’†^š’— ) š‘£+š‘¦ š‘‘š‘£/š‘‘š‘¦=(š‘£ć€–š‘¦š‘’怗^š‘£)/(š‘¦š‘’^š‘£ ) + š‘¦^2/(š‘¦š‘’^š‘£ ) v+š‘¦ š‘‘š‘£/š‘‘š‘¦=š‘£+ š‘¦/š‘’^š‘£ š‘¦ š‘‘š‘£/š‘‘š‘¦=š‘¦/š‘’^š‘£ š‘‘š‘£/š‘‘š‘¦=1/怖 š‘’怗^š‘£ 怖 š’†ć€—^š’— š’…š’—=š’…š’š Integrating Both Sides āˆ«1ā–’怖怖 š’†ć€—^š’— š‘‘š‘£ć€—= āˆ«1ā–’š‘‘š‘¦ 怖 š’†ć€—^š’—=š’š+š’„ Putting back š‘£=š‘„/š‘¦ š’†^(š’™/š’š)=š’š+š’„

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