Explanation:
(B) : Given, differential equation,
\(\mathrm{y}_{3}^{2 / 3}+2+3 \mathrm{y}_{3}+\mathrm{y}_{1}=0\)
Then, it is also written as-
\(\left(\frac{d^{3} y}{d x^{3}}\right)^{2 / 3}+2+3\left(\frac{d^{2} y}{d x^{2}}\right)+\frac{d y}{d x}=0\)
\(\left(\frac{d^{3} y}{d x^{3}}\right)^{2 / 3}=-\left[\left(\frac{d^{2} y}{d x^{2}}\right) \times 3+\frac{d y}{d x}+2\right]\)
\(\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=-\left[3 \times \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+2\right]^{3}\)
So, the degree of differential equation is 2 and order is 3 .