ode plotter.m

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