Hi, I understand that you are not able to find solution through dsolve. The function dsolve can solve differential equations when variables are separable. However you can solve this differential equation using MATLAB Numerical Solver ode45. Here is a sample code.
tspan = -5:0.5:5; % Interval of Integration
y0 = 0; % Initial Condition
[x,y] = ode45(@(x,y)odefun(x,y), tspan,y0);
plot(x,y);
function dydx = odefun(x,y)
dydx = (y + x.*(x.^2 + y.^2).^(1/2))/(x - y.*(x.^2 + y.^2).^(1/2));
end
