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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$
(ie) $\large\frac{y'}{y}$$=m$
$\therefore$ the $D. E$ is $y=e^{\Large\frac{y'}{y}x}$
answered Sep 3, 2013 by meena.p
 

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