Why does the solution contain the c1 variable even though I set the conditions?

I´m trying to plot the solution of the following differential equation but I keep getting the c1 variable restraining me from ploting the symbolic function with two variables

syms y(x)

ode = diff(y) == 2+y/x
cond = y(0) == 0 
ySol = dsolve(ode,cond)
fplot(ySol);

The solution of dsolve is ySol = C1*x + 2*x*log(x)

According to documentation specifing the initial condition should find a value of c1 and find a solution without the constant but I keep getting solution with the constant. Thank you for help

Answer 1

[David Hill]

Problem with y(0) condition (log(0) = -inf)

syms y(x)
ode = diff(y) == 2+y/x;
cond = y(.001) == 0;
ySol = dsolve(ode,cond)

ySol = 

fplot(ySol);

[Marek]

Thank you so very much!

[Torsten]

Note the difference between the correct and the "approximate" solution.

syms y(x) x
ode = diff(y) == 2+y/x;
cond = y(.001) == 0;
ySol = dsolve(ode,cond);
ySol_correct = 2*x*log(x);
figure(1)
hold on
fplot(ySol)
fplot(ySol_correct)
hold off
grid on

First get the general solution - then insert your boundary condition:

syms y(x)
ode = diff(y) == 2+y/x;
ySol(x) = dsolve(ode);
var = symvar(ySol)

var = 

C1 = solve(limit(ySol,x,0)==0,var(2));
ySol = subs(ySol,var(2),C1);
figure(2)
fplot(ySol)
grid on

[David Hill]

Excellent. Thanks for the correction.