The general solution of the differential equation $$\frac{d x}{d t}=\frac{x \log x}{t}$$ is

If $$3 \sin \theta=2 \sin 3 \theta$$ and $$0< \theta<\pi$$, then $$\sin \theta=$$

The maximum value of the objective function $$z=2 x+3 y$$ subject to the constraints $$x+y \leq 5,2 x+y \geq 4$$ and $$x \geq 0, y \geq 0$$ is

The particular solution of differential equation $$(x+y) d y+(x-y) d x=0$$ at $$x=y=1$$ is