# Find the differential equation of family of straight lines $y=mx+\large\frac{a}{m}$ When $a , m,$ both are parameters.

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• If we have an equation $f(x,y,c_1,c_2,....c_n)=u$ Containing n arbitrary constant $c_1,c_2...c_n$, then by differentiating n times, we get $(n+1)$ equations in total. If we eliminate the arbitrary constants $c_1,c_2....c_n,$ we get a D.E of order n
$y=mx+\large\frac{a}{m}$----(i) where a,m are parameters
$\large\frac{dy}{dx}$$=m \large\frac{d^2y}{dx^2}$$=0$
It is the required D. E