The degree of the differential equation

$$ x\left(\frac{d^2 y}{d x^2}\right)^{1 / 3}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{5 / 3}+7 \frac{d y}{d x}+y=0 $$

The curve that satisfies the differential equation $x y d y-\left(1+y^2\right) d x=0$ passes through $(1,0)$ and intersects the curve $x^2+3 y^2=3$ at an angle $\theta$. Then, $\frac{2 \theta}{\pi}=$

Choose the correct statement from following.

If $E$ and $E_0$ denote energies at time $t$ and $t_0$ respectively, and $L$ and $L_0$ distance from same point at $t$ and $t_0$ respectively, then which of the following equations can be declared to be incorrect on dimensional grounds? (A) $E=\frac{2 E_0 L}{L_0}$ (B) $E=E_0 e^{-2 L / L_0}$ (C) $E=2 L e^{-L / E_0}$ (D) $E=2\left(E_0 / L_0\right) \times e^{-L / L_0}$