If $\cos x \frac{d y}{d x}-y \sin x=6 x,\left(0 < x < \frac{\pi}{2}\right)$ and $y\left(\frac{\pi}{3}\right)=0$, then $y\left(\frac{\pi}{6}\right)=$

$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$

The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is

If $y=a^3 e^{y^2 x+c}$ is the general solution of a differential equation, where $a$ and $c$ are arbitrary constants and $b$ is fixed constant, then the order of differential equation is