The sum of the order and degree of the differ | vedclass

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(A) Given differential equation: $x\left(\frac{d^2 y}{d x^2}\right)^{1/2} = \left(1+\frac{d y}{d x}\right)^{4/3}$.To find the degree,we must eliminate

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Given differential equation: $x\left(\frac{d^2 y}{d x^2}\right)^{1/2} = \left(1+\frac{d y}{d x}\right)^{4/3}$.To find the degree,we must eliminate the fractional exponents.First,square both sides: $x^2 \left(\frac{d^2 y}{d x^2}\right) = \left(1+\frac{d y}{d x}\right)^{8/3}$.Next,cube both sides to remove the remaining fraction: $x^6 \left(\frac{d^2 y}{d x^2}\right)^3 = \left(1+\frac{d y}{d x}\right)^8$.Now,the equation is in polynomial form with respect to the derivatives.The highest order derivative is $\frac{d^2 y}{d x^2}$,so the order is $2$.The power of the highest order derivative is $3$,so the degree is $3$.The sum of the order and degree is $2 + 3 = 5$.

The sum of the order and degree of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{2}}=\left(1+\frac{d y}{d x}\right)^{\frac{4}{3}}$ is

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