The order and degree of the differential equa | vedclass

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Question

(A) Given the differential equation: $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$.Subtract $x\frac{dy}{dx}$ from both sides: $y

Vedclass · Accepted Answer

$1, 2$

Vedclass · Answer

(A) Given the differential equation: $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$.Subtract $x\frac{dy}{dx}$ from both sides: $y - x\frac{dy}{dx} = \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$.Squaring both sides to eliminate the square root:$(y - x\frac{dy}{dx})^2 = a^2\left(\frac{dy}{dx}\right)^2 + b^2$.Expanding the left side:$y^2 + x^2\left(\frac{dy}{dx}\right)^2 - 2xy\frac{dy}{dx} = a^2\left(\frac{dy}{dx}\right)^2 + b^2$.The highest derivative present is $\frac{dy}{dx}$,so the order is $1$.The highest power of the highest derivative after rationalizing the equation is $2$,so the degree is $2$.Thus,the order and degree are $1, 2$.

The order and degree of the differential equation $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$ are

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