Differential equations

2. For :1: 2 0, y 2 0, consider the planar system given by x'=:r(32:ry) y'=y(2-$-y) (a) Find equations for the asnullclines. (b) Find equations for the ynullclines (c) Find all equilibrium points. (d) Carefully sketch the phase plane for this system. Include the nullclines (with direction arrows) and equilibrium points you found above. In addition, carefully sketch the solution curve passing through point (1/2, 7/4), the dot on the grid, for t E (U, 00). 3