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The degree of the differential equation $\;\Large c=\frac{\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{2/3}}{\frac{d^{3}y}{dx^{3}}}$ where $c$ is a constant

\[\begin{array}{1 1}(1)1&(2)3\\(3)-2&(4)2\end{array}\]

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$C =\large\frac{\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{2/3}}{\frac{d^{3}y}{dx^{3}}}$
$C \large\frac{d^3y}{dx^3}=\bigg[1+\bigg(\frac{dy}{dx}\bigg)^{3}\bigg]^{2/3}$
Raising both sides to the powder 3
$C^3 \bigg(\large\frac{d^3y}{dx^3} \bigg)^3= \bigg[1+ \bigg( \large\frac{dy}{dx} \bigg)^3 \bigg]^2$
Order =3
degree =3
Hence 2 is the correct answer
answered May 22, 2014 by meena.p

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