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(C) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$. The order of a differential equ

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Order $2$,Degree not defined

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(C) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,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 $\cos \left(\frac{d y}{d x}\right)$ involves a transcendental function of the derivative,which means the equation cannot be expressed as a polynomial in terms of its derivatives. Therefore,the degree of this differential equation is not defined.

Determine the order and degree (if defined) of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$.

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