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TN XII Math
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Differential Equations
Form the differential equuations by eliminating arbitary constants given in brackets against each $y=e^{mx} [m] $
tnstate
class12
bookproblem
ch8
sec-1
exercise8-1
p129
q2
q2-8
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asked
Apr 15, 2013
by
poojasapani_1
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1 Answer
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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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