Question

Find the differential equation representing the family of curves v=A|r+B whrer A and B are arbitary constant

Answer 1

We have:V=Ar+B
(i)Differentiating with respect to r we get,dVdr=−Ar2 ;(ii)Again differentiating with respect to r we get,d2Vdr2=−(−2)Ar3⇒d2Vdr2=2Ar3Using (ii) we get:

d2Vdr2=2r3(−dVdr.r2)⇒d2Vdr2=−2rdVdr⇒d2Vdr2+2rdVdr=0