The order and the degree of the differential | vedclass

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Question

(A) The order of a differential equation is the order of the highest derivative present in the equation.In the given equation $\frac{d^4y}{dx^4} - 4\f

Vedclass · Accepted Answer

$4, 1$

Vedclass · Answer

(A) The order of a differential equation is the order of the highest derivative present in the equation.In the given equation $\frac{d^4y}{dx^4} - 4\frac{d^3y}{dx^3} + 8\frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 4y = 0$,the highest derivative is $\frac{d^4y}{dx^4}$,which is of order $4$.Therefore,the order of the differential equation is $4$.The degree of a differential equation is the power of the highest derivative when the equation is expressed as a polynomial in derivatives.Here,the power of the highest derivative $\frac{d^4y}{dx^4}$ is $1$.Thus,the degree is $1$.Hence,the order and degree are $4$ and $1$ respectively.

The order and the degree of the differential equation $\frac{d^4y}{dx^4} - 4\frac{d^3y}{dx^3} + 8\frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 4y = 0$ are respectively:

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