The differential equation frac{d^2y}{dx^2} + | vedclass

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Question

(D) The given differential equation is $\frac{d^2y}{dx^2} + x\frac{dy}{dx} + \sin y + x^2 = 0$.$1$. The order of a differential equation is the order

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Both $(b)$ and $(c)$

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(D) The given differential equation is $\frac{d^2y}{dx^2} + x\frac{dy}{dx} + \sin y + x^2 = 0$.$1$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^2y}{dx^2}$,so the order is $2$.$2$. The degree of a differential equation is the power of the highest derivative when the equation is expressed as a polynomial in derivatives. Since $\sin y$ is present,the equation is non-linear,but the highest derivative $\frac{d^2y}{dx^2}$ has an exponent of $1$. Thus,the degree is $1$.Therefore,the equation is of order $2$ and degree $1$. Hence,option $(d)$ is correct.

The differential equation $\frac{d^2y}{dx^2} + x\frac{dy}{dx} + \sin y + x^2 = 0$ is of the following type:

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