We know that for the function $f(x,y)=log(x^2{e}^y+(x+1)(y-1{)}^2),$

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}=\frac{2x{e}^y+(y-1{)}^2}{x^2{e}^y+(x+1)(y-1{)}^2},\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=\frac{x^2{e}^y+2(x+1)(y-1)}{x^2{e}^y+(x+1)(y-1{)}^2}$

Then what's the flow along of $[t]=(\frac{t^2}{2t^3}),0t1$ with the vector field

$F[x]=(\frac{\frac{2x{e}^y+(y-1{)}^2}{x^2{e}^{y+(x+1)(y-1{)}^2}}}{\frac{x^2{e}^y+2(x+1)(y-1)}{x^2{e}^y+(x+1)(y-1{)}^2}})$