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Differential Equations
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Find the order and degree of the following differential equation: $\big(\large\frac{dy}{dx}) ^{2} +x=\large\frac{dx}{dy}+x^{2}$
tnstate
class12
bookproblem
ch8
sec-1
exercise8-1
p128
q1
q1-9
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asked
Apr 14, 2013
by
poojasapani_1
edited
Apr 14, 2013
by
poojasapani_1
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The order of a D.E is the order of the highest order derivative occurring in it. The degree of the D.E is the degree of the highest order derivative which occurs in it, after the D.E has been made free from radicals and fractions as far as derivatives are concerned.
Given $ \bigg( \large\frac{dy}{dx}\bigg)^2$$+x=\large\frac{dx}{dy}$$+x^2$
$ \bigg( \large\frac{dy}{dx}\bigg)^2$$+x=\large\frac{1}{\Large\frac{dx}{dy}}$$+x^2$
Multiplying by $\large\frac{dy}{dx}$
$ \bigg( \large\frac{dy}{dx}\bigg)^3$$+\large\frac{dy}{dx}$$(x-x^2)-1=0$
Order = 1
Degree = 3
answered
Sep 3, 2013
by
meena.p
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