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Vector Algebra

Question
CBSEENMA12032862
Wired Faculty App

Verify that y = A cor x – B sin x is a solution of the differential equation
fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.

Solution

               straight y space equals space straight A space cosx space minus space straight B space sinx
therefore space space space dy over dx space equals space minus straight A space sinx space minus space straight B space cosx rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals space minus straight A space cosx space plus space straight B space sinx rightwards double arrow space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space minus straight y space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0 therefore space space space space straight y space equals space straight A space cosx space minus space straight B space sinx space space is space straight a space solution space of space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.

Some More Questions From Vector Algebra Chapter

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

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