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Vector Algebra

Question
CBSEENMA12035675
Wired Faculty App

If space straight y space equals space straight e to the power of ax. cosbx comma space then space prove space that space space space fraction numerator straight d squared straight y over denominator dx squared end fraction minus 2 straight a dy over dx plus left parenthesis straight a squared plus straight b squared right parenthesis straight y space equals space 0

Solution
straight y equals straight e to the power of ax. cos space bx dy over dx equals ae to the power of ax. cosbx minus be to the power of ax. sinbx space space... left parenthesis straight i right parenthesis dy over dx equals ay minus be to the power of ax. space sinbx fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight a dy over dx minus straight b left parenthesis ae to the power of ax. sinbx plus be to the power of ax. cosbx right parenthesis fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight a dy over dx minus abe to the power of ax. sinbx minus straight b squared straight e to the power of ax. cos space bx fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight a dy over dx minus straight a open parentheses ay minus dy over dx close parentheses minus straight b squared straight y space left square bracket Substituting space be to the power of ax space sinbx space from space left parenthesis straight i right parenthesis right square bracket
fraction numerator straight d squared straight y over denominator dx squared end fraction space equals straight a dy over dx minus straight a squared straight y plus straight a dy over dx minus straight b squared straight y therefore space space space fraction numerator straight d squared straight y over denominator dx squared end fraction minus 2 straight a dy over dx plus left parenthesis straight a squared plus straight b squared right parenthesis straight y space equals space 0
Hence Proved


Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = ex

Determine order and degree (if defined) of differential equations:
y'' + (y')2 + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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