Troubleshooting - A Guide to MATLAB for Beginners and Experienced Users - page 288

sol =
1/(1-exp(-t)*(-1+x0)/x0)

Note that this includes the zero solution; indeed

bettersol = simplify(sol)

bettersol =
-x0/(-x0-exp(-t)+exp(-t)*x0)

subs(bettersol, x0, 0)

ans =
0

(b)

T = 0:0.1:5;

hold on
solcurves = inline(vectorize(bettersol), 't', 'x0');
for initval = 0:0.25:2.0
plot(T, solcurves(T, initval))
end
axis tight
title 'Solutions of Dx=x-xˆ2, with x(0) = 0, 0.25,..., 2'
xlabel 't'
ylabel 'x'
hold off

Solutions of Dx = x − x 2 , with x(0) = 0, 0.25, ..., 2

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

t