Created
January 27, 2019 23:04
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syms t; | |
syms C; | |
syms y; | |
syms r; | |
syms y; | |
syms x; | |
syms Y; | |
syms X; | |
hw_problem = '2.1 #24'; | |
crange = 0:0; | |
ode = @(y, t) (y+t)/(y-t); | |
no_general = 1; | |
general_solution = 1/3 * t^2 + C/t; | |
xlab = 't'; | |
ylab = 'y(t)'; | |
trange = -5:0.2:5; | |
yrange = -5:0.2:5; | |
[tm, ym] = meshgrid(trange, yrange); | |
dt = trange(2) - trange(1); | |
odev = vectorize(ode); | |
if isa(ode,'function_handle') | |
odev = eval(odev); | |
end | |
slope = feval(odev,ym,tm); | |
hold on | |
slopet(1:length(yrange), 1:length(trange)) = dt; | |
slopey = slope * dt; | |
L = sqrt(slopet.^2 + slopey.^2); | |
quiver(trange, yrange, slopet./L, slopey./L, 0.5); | |
leg = {'Direction'}; | |
if no_general == 0 | |
i = 2; | |
for c = crange | |
fsol = matlabFunction(subs(general_solution, C, c)); | |
fplot(fsol); | |
leg{i} = strcat('C=', num2str(c)); | |
i = i + 1; | |
end | |
end | |
legend(leg, 'FontSize', 12) | |
xlabel(xlab, 'FontSize', 14) | |
ylabel(ylab, 'FontSize', 14) | |
if no_general == 0 | |
description = strcat(hw_problem, ' ODE: ', char(ode), ' General: ', char(general_solution)); | |
else | |
description = strcat(hw_problem, ' ODE: ', char(ode)); | |
end | |
title(description, 'FontSize', 18) | |
grid | |
axis([trange(1) trange(length(trange)) yrange(1) yrange(length(yrange))]) | |
hold off |
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