Example 20 - Chapter 9 Class 12 Differential Equations

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Example 20 - Find particular solution log (dy/dx) =3x + 4y - Examples

part 2 - Example 20 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations
part 3 - Example 20 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations

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Example 20 Find the particular solution of the differential equation log(š‘‘š‘¦/š‘‘š‘„)=3š‘„+4š‘¦ given that š‘¦=0 š‘¤ā„Žš‘’š‘› š‘„=0 log(š‘‘š‘¦/š‘‘š‘„)=3š‘„+4š‘¦ š’…š’š/š’…š’™ = e(3x + 4y) š‘‘š‘¦/š‘‘š‘„ = e3x e4y Separating the variables š‘‘š‘¦/š‘’^4š‘¦ = e3x dx eāˆ’4y dy = e3x dx Integrating both sides āˆ«1ā–’怖š‘’^(āˆ’4š‘¦) š‘‘š‘¦ć€—=āˆ«1ā–’š‘’^3š‘„ š‘‘š‘„ š’†^(āˆ’šŸ’š’š)/(āˆ’šŸ’)=š’†^šŸ‘š’™/šŸ‘+š‘Ŗ 0=š‘’^3š‘„/3+š‘’^(āˆ’4š‘¦)/4+š¶ š‘’^3š‘„/3 + š‘’^(āˆ’4š‘¦)/4 + C = 0 (4š‘’3š‘„" + " 3š‘’^(āˆ’4š‘¦))/12 + C = 0 (4š‘’3š‘„" + " 3š‘’^(āˆ’4š‘¦) + 12š¶)/12 " = 0" šŸ’š’†^šŸ‘š’™ + šŸ‘š’†^(āˆ’šŸ’š’š) + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4š‘’^(3(0)) + 3š‘’^(āˆ’4(0)) + 12C = 0 4š‘’^0 + 3š‘’^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = ā€“ 7 C = (āˆ’šŸ•)/šŸšŸ Putting value of C in (1) 4š‘’^3š‘„ + 3š‘’^(āˆ’4š‘¦) + 12C = 0 4š‘’^3š‘„ + 3š‘’^(āˆ’4š‘¦) + 12((āˆ’7)/12) = 0 šŸ’š’†^šŸ‘š’™ + šŸ‘š’†^(āˆ’šŸ’š’š) āˆ’ 7 = 0

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