Form the differential equation representing the family of curves y= b\, \cos \left (x+a \right ), where a and b are arbitrary constants.

 

 

 

 
 
 
 
 

Answers (1)

y= b\, \cos \left ( x+a \right )\: \: \left [ given \right ]---(1)
Differentiating w.r.t x we get \frac{dy}{dx}= -b\, \sin \left ( x+a \right )
Again differentiating w.r.t x we get
\frac{d^{2}y}{dx^{2}}= -b\, \cos \left ( x+a \right )\: or\: \frac{d^{2}y}{dx^{2}}= -y\: \: \left [ \because \, of\, \left ( 1 \right ) \right ]
which is required D.E.

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