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Question

(A) The given differential equation is $(\frac{d^3y}{dx^3})^2 + (\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^4 + y^5 = 0$. The order of a differential equa

Vedclass · Accepted Answer

Order $3$,Degree $2$

Vedclass · Answer

(A) The given differential equation is $(\frac{d^3y}{dx^3})^2 + (\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^4 + y^5 = 0$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^3y}{dx^3}$,so the order is $3$. The degree of a differential equation is the power of the highest order derivative,provided the equation is a polynomial in its derivatives. Here,the highest order derivative $\frac{d^3y}{dx^3}$ is raised to the power of $2$. Therefore,the degree is $2$.

Determine the order and degree (if defined) of the differential equation: $(\frac{d^3y}{dx^3})^2 + (\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^4 + y^5 = 0$.

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