Getting General Solution Using dsolve

I am trying to solve the equation below

ode(x) =

clc;clear
syms y(x)
RHS = (y + x*(x^2 + y^2)^(1/2))/(x - y*(x^2 + y^2)^(1/2))
ode = diff(y,x) == RHS
ysol = dsolve(ode,'IgnoreAnalyticConstraints', false)

But it is saying that it is unable to find explicit solution. In Wolfram Alpha however, the general solution came out to be

sqrt(x^2 + y(x)^2) + tan^(-1)(x/y(x)) = c_1

How do I get this in Matlab?

Answer 1

[Guru Mohanty]

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