The degree of the differential equation frac{ | vedclass

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(A) Given the differential equation: $\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx} - 3} = x$ Rearrange the equation to isolate the radical term: $\frac{d^2

Vedclass · Accepted Answer

$2$

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(A) Given the differential equation: $\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx} - 3} = x$ Rearrange the equation to isolate the radical term: $\frac{d^2y}{dx^2} - x = \sqrt{\frac{dy}{dx} - 3}$ Squaring both sides to eliminate the square root: $\left(\frac{d^2y}{dx^2} - x\right)^2 = \frac{dy}{dx} - 3$ Expanding the left side: $\left(\frac{d^2y}{dx^2}\right)^2 - 2x\frac{d^2y}{dx^2} + x^2 = \frac{dy}{dx} - 3$ 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. The highest order derivative is $\frac{d^2y}{dx^2}$,and its highest power is $2$. Therefore,the degree is $2$.

The degree of the differential equation $\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx} - 3} = x$ is

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