## anonymous one year ago Let y(x) be a solution of the initial value problem y'= y- y^2, y(0)= y0, 0<y0<1. Show that y0< y(x)<=1 for all x belongs to (0,infinity).

1. freckles

and also y has to be between 0 and 1..since $\frac{dy}{y-y^2}=dx \\ y \neq 0,1 \\ \text{ so we have three intervals } (-\infty,0) \text{ or } (0,1) \text{ or } (1,\infty) \\ \text{ but again since } 0<y_0<1 \text{ then } \\ 0<y<1 \\ \text{ so solve for } y \\ \text{ then show } y-y_0>0 \text{ for } x>0$

2. freckles

I thought it was repetitive a bit so I deleted that one post :p

3. anonymous

y= e^x/(e^x+c)