Example 39 - If y = A sin x + B cos x, prove d2y/dx2 + y = 0 - Finding second order derivatives- Implicit form

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Example 39 If = A sin +B cos , then prove that 2 2 + y = 0. = A sin +B cos Differentiating . . . = A sin + B cos = A sin + B cos = A . sin + B . cos = A cos + B ( sin ) = A cos B sin Again Differentiating . . . 2 2 = ( A cos B sin ) 2 2 = A cos + B sin 2 2 = A sin + B ( cos ) We need to show 2 2 + = 0 Solving LHS 2 2 + = ( A sin x B cos x) + (A sin x + B cos x) = 0 = RHS Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.