The order and degree of the differential equa | vedclass

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Question

(B) The order of a differential equation is the order of the highest derivative present in the equation. In the given equation,the highest derivative

Vedclass · Accepted Answer

$2, 	ext{Not defined}$

Vedclass · Answer

(B) The order of a differential equation is the order of the highest derivative present in the equation. In the given equation,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 derivative when the equation is expressed as a polynomial in its derivatives. The given equation contains the term $\sin \left(\frac{d y}{d x}\right)$,which is a transcendental function of the derivative. Since the equation cannot be expressed as a polynomial in its derivatives,the degree is not defined. Therefore,the order is $2$ and the degree is not defined.

The order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ are . . . . . . and . . . . . . respectively.

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