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# Form the differential equuations by eliminating arbitary constants given in brackets against each $y=e^{mx} [m]$

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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
Step 1:
$y= e^{mx}$-----(i)
$\large\frac{dy}{dx}$$=me^{mx}-----(ii) Step 2: (ii) divided by (i) gives \large\frac{\Large\frac{dy}{dx}}{y}$$=m$