MATLAB: How to write equation

dot slash vs. slashequation

r (y ) =(1-x^2)/(1-x*cos(y) where y= 0 to 2pi and x=(0,0.1,0.5,0.9)

   x=[0,0.1,0.5,0.9]
   y=linspace(0,2*pi,numel(x))
   r=(1-x.^2)./(1-x.*cos(y))
   plot(y,r,'-*b')

It may depend on your MATLAB version. Assuming I interpreted your equation correctly, in R2016a, this code:

syms x(t) y(t) y0
[y]=dsolve(diff(y) == exp(2*x)*cos(y)^2, y(0) == y0)

produces this result:

y =
atan(tan(y0) + int(exp(2*x(x)), x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))

Alternatively, if ‘y’ is a function of ‘x’ rather than ‘t’, this works:

syms y(x) y0
[y]=dsolve(diff(y) == exp(2*x)*cos(y)^2, y(0) == y0)
y =
atan(exp(2*x)/2 + tan(y0) - 1/2)

Choose the one that works for you.

Espen, use

 x = linspace(0,4,20);
 y = linspace(0,4,20);
 [X,Y] = meshgrid(x,y);  % create a grid of data points
 Z     = sin(pi.*X).*sin(pi.*Y);
 mesh(X,Y,Z)

Z needs to be an n-by-m, just like X and Y.