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(A) Given the differential equation: $y \left( \frac{dy}{dx} \right) = \frac{x}{\frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3}$.Multiply both sides b

Vedclass · Accepted Answer

$1$

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(A) Given the differential equation: $y \left( \frac{dy}{dx} \right) = \frac{x}{\frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3}$.Multiply both sides by $\left( \frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3 \right)$ to clear the fraction:$y \left( \frac{dy}{dx} \right) \left( \frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3 \right) = x$.Expanding this,we get:$y \left( \frac{dy}{dx} \right)^2 + y \left( \frac{dy}{dx} \right)^4 = x$.The order of a differential equation is the order of the highest derivative present in the equation.Here,the highest derivative is $\frac{dy}{dx}$,which is a first-order derivative.Therefore,the order of the differential equation is $1$.

The order of the differential equation $y \left( \frac{dy}{dx} \right) = \frac{x}{\frac{dy}{dx} + \left( \frac{dy}{dx} \right)^3}$ is

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