Find the order and degree of the differential | vedclass

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(D) The given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{2}+\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}}=\frac{d^{2}y}{dx^{

Vedclass · Accepted Answer

order $= 2$,degree is not defined

Vedclass · Answer

(D) The given differential equation is $\left[1+\left(\frac{dy}{dx}\right)^{2}+\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}}=\frac{d^{2}y}{dx^{2}}$.To find the degree,the equation must be a polynomial in terms of its derivatives.The term $\sin \left(\frac{dy}{dx}\right)$ makes the equation non-polynomial in terms of the derivative $\frac{dy}{dx}$.Therefore,the degree of this differential equation is not defined.The order of the differential equation is the highest derivative present,which is $\frac{d^{2}y}{dx^{2}}$,so the order is $2$.Thus,the correct option is $D$.

Find the order and degree of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}+\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}}=\frac{d^{2}y}{dx^{2}}$.

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