The order and the degree of the differential | vedclass

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Question

(A) Given the differential equation: $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}=7\left(\frac{d^{2}y}{dx^{2}}\right)$.To find the deg

Vedclass · Accepted Answer

$2, 3$

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(A) Given the differential equation: $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}=7\left(\frac{d^{2}y}{dx^{2}}\right)$.To find the degree,we must eliminate the fractional exponent. Raise both sides to the power of $3$:$\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{7} = 7^{3}\left(\frac{d^{2}y}{dx^{2}}\right)^{3}$.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 order derivative after the equation is expressed as a polynomial in derivatives. Here,the power of $\frac{d^{2}y}{dx^{2}}$ is $3$.Thus,the order is $2$ and the degree is $3$.

The order and the degree of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}=7\left(\frac{d^{2}y}{dx^{2}}\right)$ are respectively

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