The order and degree of the differential equa | vedclass

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(D) Given differential equation is $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$. Rearranging the terms,we get $\sqrt{\frac{dy}{dx}} = 4\frac{dy}{d

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$1$ and $2$

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(D) Given differential equation is $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$. Rearranging the terms,we get $\sqrt{\frac{dy}{dx}} = 4\frac{dy}{dx} + 7x$. Squaring both sides to remove the radical,we obtain $\frac{dy}{dx} = (4\frac{dy}{dx} + 7x)^2$. Expanding the right side,we get $\frac{dy}{dx} = 16(\frac{dy}{dx})^2 + 49x^2 + 56x\frac{dy}{dx}$. The highest derivative present is $\frac{dy}{dx}$,so the order is $1$. The highest power of the highest derivative after making the equation a polynomial in derivatives is $2$,so the degree is $2$. Thus,the order is $1$ and the degree is $2$.

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$ are

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