Statement 1: The degrees of the differential | vedclass

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Question

(D) For Statement $1$:Consider the first differential equation: $\frac{dy}{dx} + y^2 = x$. The highest order derivative is $\frac{dy}{dx}$ (order $1$)

Vedclass · Accepted Answer

Statement $1$ is true,Statement $2$ is true; Statement $2$ is a correct explanation of Statement $1$.

Vedclass · Answer

(D) For Statement $1$:Consider the first differential equation: $\frac{dy}{dx} + y^2 = x$. The highest order derivative is $\frac{dy}{dx}$ (order $1$),and its power is $1$. Thus,the degree is $1$.Consider the second differential equation: $\frac{d^2y}{dx^2} + y = \sin x$. The highest order derivative is $\frac{d^2y}{dx^2}$ (order $2$),and its power is $1$. Thus,the degree is $1$.Since both equations have a degree of $1$,Statement $1$ is true.For Statement $2$:This is the standard definition of the degree of a differential equation. It is a polynomial in derivatives,and the degree is the highest power of the highest order derivative. Thus,Statement $2$ is true.Conclusion:Statement $2$ provides the definition used to determine the degrees in Statement $1$,making it the correct explanation. Therefore,the correct option is $D$.

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