Homogeneous differential equation with dsolve => Warning: Unable to find explicit solution.

Hey,

I would like to understand why I get this message "Warning: Unable to find explicit solution" when I try to get the ODE solution.

I'm following the steps in the Help Center - Solve Differential Equation.

I hope you can help me.

clear all; close all; clc;

syms y(x)   
Dy = diff(y);
ODE = diff(y,x,2) == ( x^2 + y^2 ) / ( x*y ) ;

cond1 = y(0)   == 3;
cond2 = Dy(0)  == 0;
conds = [cond1, cond2];

ySol(x) = dsolve(ODE,conds);
ySol = simplify(ySol)

% Command Window

Warning: Unable to find explicit solution. 
> In dsolve (line 201)
  In ignore (line 12) 
 
ySol(x) =
 
[ empty sym ]
 
>>

Answer 1

[Star Strider]

The differential equation is nonlinear. There are only a few nonlinear differential equations that have analytical solutions. This is not one of them.

Try this instead —

syms y(x) x Y  
Dy = diff(y);
ODE = diff(y,x,2) == ( x^2 + y^2 ) / ( x*y ) ;
cond1 = y(0)   == 3;
cond2 = Dy(0)  == 0;
[VF,Sbs] = odeToVectorField(ODE)

VF = 

Sbs = 

odefcn = matlabFunction(VF, 'Vars',{x,Y})

odefcn = function_handle with value:
    @(x,Y)[Y(2);(Y(1).^2+x.^2)./(x.*Y(1))]

[x,y] = ode45(odefcn, [eps 10], [3 0]);

figure
plot(x,y,'-')
grid
xlabel('x')
ylabel('y')
legend(string(Sbs), 'Location','best')

The ‘tspan’ argument cannot begin at ‘x=0’ because in that situaiton, all except the initial values are NaN.