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Q.
The degree and order of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{{7}/{3}} = 7 \left(\frac{d^{2}y}{dx^{2}}\right)$ respectively are
Given, differential equation is
$\left[1+\left(\frac{d y}{d x}\right)\right]^{\frac{7}{3}}=7\left(\frac{d^{2} y}{d x^{2}}\right)$
On cubing both sides, we get
$\left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7}=7^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{3}$
Here, we see that highest order derivative is $2$, whose degree is $3$.
Hence, degree $= 3$ end order $=2$