Unable to find symbolic solution

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I'm getting this error when I'm running my code. "Unable to find symbolic solution". Can you please help me?
clear; syms y(x)
Dy = diff(y);
D2y = diff(y,2);
ode = y+((0.05*Dy)/y)-((0.5*D2y*x)/y)-(0.2/x)-(0.05/x) == 0;
ySol = dsolve(ode , y(80) == 0);
  1 Comment
John D'Errico
John D'Errico on 23 Mar 2023
syms y(x)
Dy = diff(y);
D2y = diff(y,2);
ode = y+((0.05*Dy)/y)-((0.5*D2y*x)/y)-(0.2/x)-(0.05/x) == 0
ode(x) = 
Why do you think a solution exists in the first place? Anyway, you have supplied only one boundfary condition, and this is a second order ODE, so you could not even find a numerical solution.

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Accepted Answer

Star Strider
Star Strider on 23 Mar 2023
The system is nonlinear, so it quite likely does not have an analytic solutioon.
Try something like this—
syms y(x) x Y
Dy = diff(y);
D2y = diff(y,2);
ode = y+((0.05*Dy)/y)-((0.5*D2y*x)/y)-(0.2/x)-(0.05/x)
ode(x) = 
% ySol = dsolve(ode , y(80) == 0)
[VF,Subs] = odeToVectorField(ode)
VF = 
Subs = 
odefcn = matlabFunction(VF, 'Vars',{x,Y})
odefcn = function_handle with value:
@(x,Y)[Y(2);(1.0./x.^2.*(x.*Y(2)-Y(1).*5.0+x.*Y(1).^2.*2.0e+1))./1.0e+1]
tspan = [80 0]; % Begin Solution At 80 And Go Backwards
ic = [0 eps]; % Supply Appropriate Initial Conditions, Specifically For 'Dy'
[x,y] = ode45(odefcn, tspan, ic);
figure
plot(x, y)
grid
legend(string(Subs), 'Location','best')
.

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