The order and degree of the differential equa | vedclass

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Question

(B) Given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}=7 \frac{d^{2}y}{dx^{2}}$.To find the degree,we must el

Vedclass · Accepted Answer

$2, 3$

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(B) Given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}=7 \frac{d^{2}y}{dx^{2}}$.To find the degree,we must eliminate the fractional exponent by raising both sides to the power of $3$:$\left(\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{\frac{7}{3}}\right)^{3} = \left(7 \frac{d^{2}y}{dx^{2}}\right)^{3}$.This simplifies to $\left[1+\left(\frac{dy}{dx}\right)^{3}\right]^{7} = 343 \left(\frac{d^{2}y}{dx^{2}}\right)^{3}$.The highest order derivative present is $\frac{d^{2}y}{dx^{2}}$,so the order is $2$.The power of the highest order derivative after making the equation a polynomial in derivatives is $3$,so the degree is $3$.Thus,the order and degree are $2$ and $3$ respectively.

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

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