%steven pitman

%clear screen and memory
clear, clc

%define the function
yprime = @(x,y) -(3*x.^2).*y;

%define solution curves
f1 =@(x) 2*exp(-x.^3);
f2 =@(x) 1*exp(-x.^3);
f3 =@(x) 1*exp(-x.^3);
f4 =@(x) 3*exp(-x.^3);
f5 =@(x) 4*exp(-x.^3);

%define points to determine slope
xx = [0:.2:3]';
yy = [0:.2:3];


%x and y components of the slope vectors
dy = yprime(xx,yy);
dx = ones(size(dy));

%vector to normalize slope
L=sqrt(1+dy.^2);

%plot the slope field and solution curves
figure();
hold on
quiver(xx,yy,dx./L,dy./L)
xlim([0,3])
ylim([0,3])

fplot(f1,[0,3],'LineWidth',2);
fplot(f2,[0,3],'LineWidth',2);
fplot(f3,[0,3],'LineWidth',2);
fplot(f4,[0,3],'LineWidth',2);
fplot(f5,[0,3],'r','LineWidth',2);

hold off