$200+100 \mathrm{e}^{\frac{\mathrm{t}}{2}}$

$200-100 \mathrm{e}^{\frac{1}{2}}$

$300-100 \mathrm{e}^{\frac{1}{2}}$

$300+100 \mathrm{e}^{\frac{1}{2}}$

$x=\log (x+y+2)+\mathrm{c}$, where c is the constant of integration

$x=\log (x+y-2)+\mathrm{c}$, where c is the constant of integration

$y=\log (x+y+2)+c$, where $c$ is the constant of integration

$y=\log (x+y-2)+\mathrm{c}$, where c is the constant of integration