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Question

(A) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2} = \cos 3x + \sin 3x$.The order of a differential equation is the orde

Vedclass · Accepted Answer

Order $2$,Degree $2$

Vedclass · Answer

(A) The given differential equation is $\left(\frac{d^{2} y}{d x^{2}}\right)^{2} = \cos 3x + \sin 3x$.The order of a differential equation is the order of the highest derivative present in the equation.Here,the highest derivative is $\frac{d^{2} y}{d x^{2}}$,so the order is $2$.The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in its derivatives.In the given equation,the highest order derivative $\frac{d^{2} y}{d x^{2}}$ is raised to the power of $2$.Therefore,the degree is $2$.

Determine the order and degree (if defined) of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{2} = \cos 3x + \sin 3x$.

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