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CBSE Class 12-science Answered

If y = ex sin x , prove that d2y/dx2 – 2 dy/dx  + 2y = 0 Explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:07: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove colon space fraction numerator straight d squared straight y over denominator dx squared end fraction space minus space 2 dy over dx space plus space 2 straight y space equals space 0
straight y space equals space straight e to the power of straight x sinx space
dy over dx space equals space straight d over dx open parentheses straight e to the power of straight x sinx space close parentheses space
space space space space space space equals straight e to the power of straight x space straight d over dx sinx space plus space sinx space straight d over dx straight e to the power of straight x space space space space space space... open parentheses straight d over dx straight u. straight v space equals space straight u straight d over dx straight v space space plus space straight v straight d over dx straight u space close parentheses
space space space space space space equals straight e to the power of straight x space cosx space plus space sinx space straight e to the power of straight x
space space space space space space equals straight e to the power of straight x space left parenthesis sinx space plus space cosx right parenthesis space space....... left parenthesis 1 right parenthesis
fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space straight d over dx open parentheses dy over dx close parentheses
space space space space space space space equals straight d over dx space straight e to the power of straight x space left parenthesis sinx space plus space cosx right parenthesis space
space space space space space space space equals straight e to the power of straight x open parentheses cosx space minus space sinx close parentheses space plus space left parenthesis sinx space plus space cosx right parenthesis straight e to the power of straight x
space space space space space space space equals 2 straight e to the power of straight x cosx space space space space....... left parenthesis 2 right parenthesis

straight L. straight H. straight S space equals space fraction numerator straight d squared straight y over denominator dx squared end fraction space minus space 2 dy over dx space plus space 2 straight y space
space space space space space space space space space equals 2 straight e to the power of straight x cosx space minus space 2 open square brackets straight e to the power of straight x space left parenthesis sinx space plus space cosx right parenthesis close square brackets space plus space 2 straight e to the power of straight x sinx space space space... from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
space space space space space space space space space equals 0
space space space space space space space space space equals straight R. straight H. straight S
Hence space proved.
end style
Answered by Yasmeen Khan | 27 Aug, 2018, 01:10: PM
CBSE 12-science - Maths
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