Question

Family y = Ax + A³ of curves will correspond to a differential equation of order _______________ and degree _______________.

Answer 1

Given: y = Ax + A³

Here, A is the only parameter.

Therefore, the order of the differential equation is 1.

$$\begin{gathered} y=Ax+A^3...\left(1\right) \\ \mathrm{Differentiating}\mathrm{both}\mathrm{sides}\mathrm{w}.\mathrm{r}.\mathrm{t}.x \\ \Rightarrow \frac{dy}{dx}=A...\left(2\right) \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}A\mathrm{in}\left(1\right) \\ \Rightarrow y=\frac{dy}{dx}x+{\left(\frac{dy}{dx}\right)}^3 \end{gathered}$$

Here, the power of the highest order derivative is 3.

Hence, family y = Ax + A³ of curves will correspond to a differential equation of order 1 and degree 3.