If m and n are the degree and order of the di | vedclass

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(C) The given differential equation is $\left(1+\left(\frac{dy}{dx}\right)^{2}\right)^{2/3} = \frac{d^{2}y}{dx^{2}}$.To find the degree,we must elimin

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$5$

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(C) The given differential equation is $\left(1+\left(\frac{dy}{dx}\right)^{2}\right)^{2/3} = \frac{d^{2}y}{dx^{2}}$.To find the degree,we must eliminate the fractional exponent by cubing both sides:$\left(1+\left(\frac{dy}{dx}\right)^{2}\right)^{2} = \left(\frac{d^{2}y}{dx^{2}}\right)^{3}$.The order $n$ is the highest derivative present,which is $\frac{d^{2}y}{dx^{2}}$,so $n = 2$.The degree $m$ is the power of the highest derivative after rationalizing,which is $3$,so $m = 3$.Now,calculate the required value: $\frac{m+n}{m-n} = \frac{3+2}{3-2} = \frac{5}{1} = 5$.

If $m$ and $n$ are the degree and order of the differential equation $\left(1+y_{1}^{2}\right)^{2 / 3}=y_{2}$,then the value of $\frac{m+n}{m-n}$ is

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