Differential Equations
1. Create a direction field for y 0 = y ? y 2 .
(a) You should find any equilibrium solutions by hand and atleast a few other solutions. Feel free to make a direction fieldwith some piece of technology and share a picture of it.
(b) Find at least a few solution curves and describe thebehavior of y as x ? ?, for different ranges of initial valuesy(x0) = y0.
(c) Use your direction field to approximate the value of y(0.5)if the initial condition is y(0) = 0.5.
(d) Use Euler’s method with h = 0.1 to approximate y(0.5) whenthe initial condition is y(0) = 0.5.
(e) Bonus: Find the analytical solution to this differentialequation with initial condition y(0) = 0.5 and then find the exactvalue of y, what is your percent error from your Euler methodapproximation?
