The order and degree of the differential equa | vedclass

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Question

(C) The given differential equation is $x\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 + y^2 = 0$. The order of a differential equation is the or

Vedclass · Accepted Answer

$2$ and $1$

Vedclass · Answer

(C) The given differential equation is $x\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 + y^2 = 0$. The order of a differential equation is the order of the highest derivative present in the equation. Here,the highest derivative is $\frac{d^2y}{dx^2}$,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 derivatives. Here,the power of $\frac{d^2y}{dx^2}$ is $1$. Therefore,the order is $2$ and the degree is $1$.

The order and degree of the differential equation $x\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^2 + y^2 = 0$ are respectively:

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