For the differential equation left[1-left(fra | vedclass

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(B) Given the differential equation: $\left[1-\left(\frac{dy}{dx}\right)^2\right]^{5/2} = 8 \frac{d^2y}{dx^2}$.To find the degree,we must eliminate th

Vedclass · Accepted Answer

$2$ and $2$

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(B) Given the differential equation: $\left[1-\left(\frac{dy}{dx}\right)^2\right]^{5/2} = 8 \frac{d^2y}{dx^2}$.To find the degree,we must eliminate the fractional exponent by squaring both sides:$\left[\left[1-\left(\frac{dy}{dx}\right)^2\right]^{5/2}\right]^2 = \left[8 \frac{d^2y}{dx^2}\right]^2$$\left[1-\left(\frac{dy}{dx}\right)^2\right]^5 = 64 \left(\frac{d^2y}{dx^2}\right)^2$.The highest order derivative present is $\frac{d^2y}{dx^2}$,so the order is $2$.The power to which the highest order derivative is raised after rationalizing the equation is $2$,so the degree is $2$.

For the differential equation $\left[1-\left(\frac{dy}{dx}\right)^2\right]^{5/2} = 8 \frac{d^2y}{dx^2}$,the order and degree are:

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