y = linspace(0,1);

subplot(311);
x = asin(sqrt(y)) - sqrt(y).*sqrt(1-y);
plot(x,y);
axis([0 1.5 0 1]);
xlabel('x'); ylabel('y');
title('u(y) = sqrt(y-y_0)');

subplot(312);
x = 1 - sqrt(1-y.^2);
plot(x,y);
axis([0 1.5 0 1]);
xlabel('x'); ylabel('y');
title('u(y) = a*y');

subplot(313);
y = linspace(1,50);
x = log( (sqrt(y.^2-1)+y) );
plot(x,y);
xlabel('x'); ylabel('y');
title('u(y) = a/y');