The order and degree of the differential equa | vedclass

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Question

(C) Given differential equation is $\frac{d^2 y}{d x^2} = \left(1 + \left(\frac{d y}{d x}\right)^2\right)^{1/3}$.To find the degree,we must eliminate

Vedclass · Accepted Answer

$2, 3$

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(C) Given differential equation is $\frac{d^2 y}{d x^2} = \left(1 + \left(\frac{d y}{d x}\right)^2\right)^{1/3}$.To find the degree,we must eliminate the fractional exponent by cubing both sides:$\left(\frac{d^2 y}{d x^2}\right)^3 = 1 + \left(\frac{d y}{d x}\right)^2$.The order of the highest derivative present is $2$,so the order is $2$.The power of the highest 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 $\frac{d^2 y}{d x^2} = \sqrt[3]{1 + \left(\frac{d y}{d x}\right)^2}$ are . . . . . . respectively.

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