Question #59c18

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Answer 1 · 2017-04-28T11:51:21

$\frac{d^{2} y}{{d x}^{2}} = 0 .$ $(d^2y)/dx^2=0.$

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.