The order and degree of the differential equa | vedclass

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(D) The given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2}y}{dx^{2}}$.To find the degree,we must

Vedclass · Accepted Answer

$2, 3$

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(D) The given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2}y}{dx^{2}}$.To find the degree,we must eliminate the fractional exponent by raising both sides to the power of $3$:$\left[\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{\frac{1}{3}}\right]^{3}=\left(\frac{d^{2}y}{dx^{2}}\right)^{3}$.This simplifies to $1+\left(\frac{dy}{dx}\right)^{5}=\left(\frac{d^{2}y}{dx^{2}}\right)^{3}$.The order of a differential equation is the highest derivative present,which is $\frac{d^{2}y}{dx^{2}}$,so the order is $2$.The degree is the power of the highest derivative after the equation is made free from radicals and fractions,which is $3$.Therefore,the order and degree are $2$ and $3$ respectively.

The order and degree of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2}y}{dx^{2}}$ are respectively

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