% plots for week 2 homework

x=linspace(-5,5,100);
y1=2-1./((x.^2+1).^(3/2));
y2=2+1./((x.^2+1).^(3/2));
y3=2+3./((x.^2+1).^(3/2));

plot(x,y1,x,y2,'--',x,y3,':'), shg
grid on
xlabel('x')
ylabel('y')
legend('y(0)=1','y(0)=3','y(0)=5')
title('Solutions to (x^2+1)y''+3xy=6x')