Question

Consider the solution of the differential equation y?'=-y passing through y(0)=0.5 .

A. Sketch the slope field for this differential equation,and sketch the solution passing through the point (0,0.5).

B. Use Euler's method with step size (delta)x=0.2 toestimate the solution at x=0.2,0.4,...,1 , using these to fill in thefollowing table. (Be sure not to round your answers ateach step!)

x=	0	0.2	0.4	0.6	0.8	1.0
y?	0.5

C. Plot your estimated solution on your slope field.Compare the solution and the slope field. Is the estimated solutionan over or under estimate for the actual solution?
A. over
B. under

D. Check that y=0.5e-1xis a solution to y'=-y with y(0)=0.5