The order and degree of the differential equa | vedclass

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Question

(C) The given differential equation is $\frac{d^2y}{dx^2} = \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$.To find the degree,we must eliminate the radical

Vedclass · Accepted Answer

$2, 2$

Vedclass · Answer

(C) The given differential equation is $\frac{d^2y}{dx^2} = \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$.To find the degree,we must eliminate the radical sign by squaring both sides:$\left(\frac{d^2y}{dx^2}\right)^2 = 1 + \left(\frac{dy}{dx}\right)^2$.The order of a differential equation is the highest derivative present,which is $2$ here.The degree is the power of the highest derivative after the equation is made free from radicals and fractions,which is $2$ here.Thus,the order is $2$ and the degree is $2$.

The order and degree of the differential equation $\frac{d^2y}{dx^2} = \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ are

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