Example 2 - Chapter 9 Class 12 Differential Equations

Last updated at July 14, 2026 by

Example 2 - Verify that y = e-3x is a solution of y'' + y' - 6y = 0 - Examples

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

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Example 2 Verify that the function š‘¦=š‘’^(āˆ’3š‘„) is a solution of the differential equation (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )+š‘‘š‘¦/š‘‘š‘„āˆ’6š‘¦=0 š‘¦=š‘’^(āˆ’3š‘„) š’…š’š/š’…š’™=š‘‘(š‘’^(āˆ’3š‘„) )/š‘‘š‘„ š‘‘š‘¦/š‘‘š‘„=怖āˆ’3 š‘’怗^(āˆ’3š‘„) (š’…^šŸ š’š)/(š’…š’™^šŸ )=š‘‘/š‘‘š‘„ (š‘‘š‘¦/š‘‘š‘„) =š‘‘(怖āˆ’3 š‘’怗^(āˆ’3š‘„) )/š‘‘š‘„ =āˆ’3 š‘‘(š‘’^(āˆ’3š‘„) )/š‘‘š‘„ =āˆ’3 Ɨ (怖āˆ’3 š‘’怗^(āˆ’3š‘„) ) = 怖9 š‘’怗^(āˆ’3š‘„) Now, we have to verify (š’…^šŸ š’š)/(š’…š’™^šŸ )+š’…š’š/š’…š’™āˆ’šŸ”š’š=šŸŽ Solving L.H.S (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )+š‘‘š‘¦/š‘‘š‘„āˆ’6š‘¦ Putting values = 怖9 š‘’怗^(āˆ’3š‘„)+(āˆ’3š‘’^(āˆ’3š‘„) )āˆ’6(š‘’^(āˆ’3š‘„) ) =怖9 š‘’怗^(āˆ’3š‘„)āˆ’3š‘’^(āˆ’3š‘„)āˆ’6š‘’^(āˆ’3š‘„) =怖9 š‘’怗^(āˆ’3š‘„)āˆ’9š‘’^(āˆ’3š‘„) =šŸŽ = R.H.S āˆ“ Hence Verified

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