Example 6 - Chapter 9 Class 12 Differential Equations

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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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