The degree and order of the differential equa | vedclass

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(B) The given differential equation is $y = x(\frac{dy}{dx})^2 + \frac{dy}{dx}$.To find the order and degree, we first express the equation in a form

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$2, 1$

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(B) The given differential equation is $y = x(\frac{dy}{dx})^2 + \frac{dy}{dx}$.To find the order and degree, we first express the equation in a form where the derivatives are free from radicals and fractions.The highest order derivative present in the equation is $\frac{dy}{dx}$, which is of order $1$.Since the highest order derivative is $\frac{dy}{dx}$, the order of the differential equation is $1$.The degree of a differential equation is the power of the highest order derivative when the equation is written as a polynomial in derivatives.Here, the highest power of the derivative $\frac{dy}{dx}$ is $2$.Therefore, the degree is $2$ and the order is $1$.

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

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