For the differential equation frac{d^3y}{dx^3 | vedclass

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Question

(C) Step $1$: The order of a differential equation is the order of the highest derivative present in the equation. Here, the highest derivative is $\f

Vedclass · Accepted Answer

Order = $3$, degree is not defined

Vedclass · Answer

(C) Step $1$: The order of a differential equation is the order of the highest derivative present in the equation. Here, the highest derivative is $\frac{d^3y}{dx^3}$, so the order is $3$.Step $2$: The degree of a differential equation is the power of the highest derivative, provided the equation is a polynomial in terms of derivatives. Here, the term $\cos \left( \frac{d^2y}{dx^2} \right)$ is a transcendental function of the derivative, meaning the equation cannot be expressed as a polynomial in terms of its derivatives.Step $3$: Therefore, the degree of this differential equation is not defined.

For the differential equation $\frac{d^3y}{dx^3} + \cos \left( \frac{d^2y}{dx^2} \right) = 0$, which of the following is true?

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