Question #59c18

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Answer 1 · 2017-04-28T11:51:21

# (d^2y)/dx^2=0.#

The General Eqn. of a line is,

#ax+by+c=0, a^2+b^2ne0; a,b in RR.......(l).#

#because,# the Origin #O(0,0) in l rArr a(0)+b(0)+c=0. i.e., c=0.#

Thus, the Family of Straight Lines through O(0,0) is

#L={ax+by=0 | a^2+b^2ne0; a,b in RR}.#

Since there are #2# arbitray consts., (i.e., #a and b)# we have to

costruct a Diff. Eqn. of order #2.#

Diff.ing #ax+by=0# w.r.t. #x, a+bdy/dx=0.#

Rediff.ing, #b(d^2y)/dx^2=0.#

#:. (d^2y)/dx^2=0,# is the desired Diff. Eqn.