The order and degree of the differential equa | vedclass

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(A) 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

Vedclass · Accepted Answer

$1, 2$

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(A) 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 eliminate the square root,we get $\frac{dy}{dx} = (4\frac{dy}{dx} + 7x)^2$. Expanding the right side,$\frac{dy}{dx} = 16(\frac{dy}{dx})^2 + 56x\frac{dy}{dx} + 49x^2$. The highest order derivative present is $\frac{dy}{dx}$,so the order is $1$. The highest power of the highest order derivative after making the equation a polynomial in derivatives is $2$. Therefore,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 respectively:

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