The order and degree of the differential equa | vedclass

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Question

(C) Given the differential equation: $\left(1+\frac{dy}{dx}\right)^{\frac{1}{3}}=\left(\frac{d^2y}{dx^2}\right)^{\frac{1}{2}}$To eliminate the fractio

Vedclass · Accepted Answer

$2, 3$

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(C) Given the differential equation: $\left(1+\frac{dy}{dx}\right)^{\frac{1}{3}}=\left(\frac{d^2y}{dx^2}\right)^{\frac{1}{2}}$To eliminate the fractional exponents,we raise both sides to the power of $6$ (the least common multiple of $2$ and $3$):$\left(\left(1+\frac{dy}{dx}\right)^{\frac{1}{3}}\right)^6 = \left(\left(\frac{d^2y}{dx^2}\right)^{\frac{1}{2}}\right)^6$$\left(1+\frac{dy}{dx}\right)^2 = \left(\frac{d^2y}{dx^2}\right)^3$The highest order derivative present is $\frac{d^2y}{dx^2}$,so the order is $2$.The power to which the highest order derivative is raised 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 $\left(1+\frac{dy}{dx}\right)^{\frac{1}{3}}=\sqrt{\frac{d^2y}{dx^2}}$ are respectively.

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