How to calculate differential equation with trigonometric function?

How can I solve this differential equation using matlab? The answer can be in analytical, symbolic or numerical solution form. This is what I have done:

syms y(x)

ff=1+((2/y)*x+(x^2)*(y^2)*cos(y))*diff(y,x)==0;

y(x)=dsolve(ff)

And it shows y(x) = [empty sym], which is not a proper answer that I was requires to get. Also, I've tried using other solution methods:

f=@(x,y) ((2/y)*x+(x^2)*(y^2)*cos(y))*diff(y,x)==0;

[x,y]=ode45(@(x,y),f,[0 2],1);

plot(x,y)

But this shows invalid expression error and I don't know where the problem is.

Answer 1

[KSSV]

f = @(x,y) -1./((2./y).*x+x.^2*y.^2.*cos(y)) ; 
xspan = [0.1 2] ;
x0 = 1 ;
[x,y] = ode45(f, xspan, x0);

plot(x,y)

Answer 2

[Sam Chak]

With the given ODE

function dydx = odefcn(x, y)

fcn = 2*x/y + (x^2)*(y^2)*cos(y);

dydx = - 1/fcn;

end

you can run the ode45 solver and plot the output. Note that or else singularity occurs.

h      = 1e-4;      
xspan  = 0.1:h:10;	% simulation x-range
init   = 1;
[x, y] = ode45(@(x, y) odefcn(x, y), xspan, init);

plot(x, y, 'linewidth', 1.5)
grid on
xlabel({'$x$'}, 'Interpreter', 'latex')
ylabel({'$y$'}, 'Interpreter', 'latex')
title('System response')