The family of curves y = Ax + A^3 is represen | vedclass

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(A) Given the equation of the family of curves: $y = Ax + A^3$. Differentiating both sides with respect to $x$,we get: $\frac{dy}{dx} = A$. Substituti

Vedclass · Accepted Answer

$3$

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(A) Given the equation of the family of curves: $y = Ax + A^3$. Differentiating both sides with respect to $x$,we get: $\frac{dy}{dx} = A$. Substituting $A = \frac{dy}{dx}$ back into the original equation,we obtain the differential equation: $y = x \left( \frac{dy}{dx} \right) + \left( \frac{dy}{dx} \right)^3$. The degree of a differential equation is the highest power of the highest-order derivative when the equation is expressed as a polynomial in derivatives. Here,the highest-order derivative is $\frac{dy}{dx}$,and its highest power is $3$. Therefore,the degree of the differential equation is $3$.

The family of curves $y = Ax + A^3$ is represented by a differential equation of degree:

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