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

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

The general solution of the differential equation $$\frac{d y}{d x}=2^{y-x}$$ is

If the surrounding air is kept at $$25^{\circ} \mathrm{C}$$ and a body cools from $$80^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 30 minutes, then temperature of the body after one hour will be