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Vector Algebra

Question
CBSEENMA12032935
Wired Faculty App

Find the differential equation of the family of curves  y = A sin mx + B cos mx. where m is fixed, and A and B are arbitrary constants.

Solution

The given equation is
            y = A sin mx + B cos mx.                               ...(1)
therefore space space space dy over dx equals space straight m space straight A space sin space mx space plus space straight m space straight B space cos space mx
rightwards double arrow space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space straight m squared straight A space cos space mx space minus space straight m squared space straight B space sin space mx rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space minus straight m squared left parenthesis straight A space cos space mx space plus space straight B space sin space mx right parenthesis rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals space minus straight m squared 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 open square brackets because space of space left parenthesis 1 right parenthesis close square brackets rightwards double arrow space space space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight m squared straight y space equals 0
                         

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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