The order and degree of the differential equa | vedclass

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Question

(D) The given differential equation is $\frac{d^2y}{dx^2} = \cos \left( \frac{dy}{dx} \right) + xy$. The order of a differential equation is the order

Vedclass · Accepted Answer

$2, 	ext{not defined}$

Vedclass · Answer

(D) The given differential equation is $\frac{d^2y}{dx^2} = \cos \left( \frac{dy}{dx} \right) + xy$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^2y}{dx^2}$,so the order is $2$. The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in its derivatives. In this equation,the term $\cos \left( \frac{dy}{dx} \right)$ involves a transcendental function of the derivative $\frac{dy}{dx}$,which means the equation cannot be expressed as a polynomial in its derivatives. Therefore,the degree of the differential equation is not defined.

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

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