Example 6 - Chapter 9 Class 12 Differential Equations

Last updated at December 16, 2024 by

Example 6 - Find particular solution: dy/dx = 4xy2 - Examples - Examples

part 2 - Example 6 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations
part 3 - Example 6 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations

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Example 6 Find the particular solution of the differential equation š‘‘š‘¦/š‘‘š‘„=āˆ’4š‘„š‘¦^2 given that š‘¦=1 , š‘¤ā„Žš‘’š‘› š‘„=0Given differential equation , š‘‘š‘¦/š‘‘š‘„=āˆ’4š‘„š‘¦^2 š’…š’š/š’š^šŸ = (āˆ’4 x) dx Integrating both sides. āˆ«1ā–’š‘‘š‘¦/š‘¦^2 = āˆ«1ā–’怖āˆ’4š‘„ š‘‘š‘„怗 āˆ«1ā–’š’…š’š/š’š^šŸ = āˆ’4 āˆ«1ā–’怖š’™ š’…š’™ć€— š‘¦^(āˆ’2+1)/(āˆ’2+1) = āˆ’4.š‘„^2/2 + c āˆ’ šŸ/š’š = ā€“2x2 + c y = (āˆ’1)/(āˆ’2š‘„2 + š‘) y = (āˆ’1)/(āˆ’(2š‘„2 āˆ’ š‘)) y = šŸ/(šŸš’™šŸ āˆ’ š’„) Given that at x = 0, y = 1 Putting x = 0, y = 1, in (1) 1 = 1/(2(0)^2 ) āˆ’ c 1 = 1/(āˆ’š¶) c = āˆ’1 Putting c = āˆ’1 in (1) y = 1/(2š‘„^2 ) āˆ’(āˆ’1) y = šŸ/(šŸš’™^šŸ + šŸ) Hence, the particular solution of the equation is y = šŸ/(šŸš’™^šŸ + šŸ)

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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 and Computer Science at Teachoo