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(C) The given differential equation is:$\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0$The order of a differential equation is th

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Order $4$,Degree not defined

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(C) The given differential equation is:$\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0$The order of a differential equation is the order of the highest derivative present in the equation.Here,the highest derivative is $\frac{d^{4} y}{d x^{4}}$,so the order is $4$.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.Since the term $\sin \left(\frac{d^{3} y}{d x^{3}}\right)$ involves a transcendental function of a derivative,the equation cannot be expressed as a polynomial in its derivatives.Therefore,the degree of this differential equation is not defined.

For the differential equation given below,determine its order and degree (if defined).
$\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0$

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For the differential equation given below,determine its order and degree (if defined).$\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0$