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(A) The given differential equation is:$\left(\frac{dy}{dx}\right)^{3}-4\left(\frac{dy}{dx}\right)^{2}+7y=\sin x$The highest order derivative present

Vedclass · Accepted Answer

Order: $1$,Degree: $3$

Vedclass · Answer

(A) The given differential equation is:$\left(\frac{dy}{dx}\right)^{3}-4\left(\frac{dy}{dx}\right)^{2}+7y=\sin x$The highest order derivative present in the equation is $\frac{dy}{dx}$,which is a first-order derivative.Therefore,the order of the differential equation is $1$.The degree of a differential equation is the highest power of the highest order derivative when the equation is expressed as a polynomial in derivatives.Here,the highest power of the first-order derivative $\frac{dy}{dx}$ is $3$.Therefore,the degree of the differential equation is $3$.

For the differential equation given below,determine its order and degree (if defined):
$\left(\frac{dy}{dx}\right)^{3}-4\left(\frac{dy}{dx}\right)^{2}+7y=\sin x$

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For the differential equation given below,determine its order and degree (if defined):$\left(\frac{dy}{dx}\right)^{3}-4\left(\frac{dy}{dx}\right)^{2}+7y=\sin x$