differential equation

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Indeed, if you want to plot $g(x)$, the expression $g(x)$ should evaluate to a number when $x$ is a number. You correctly determined that the presence of the symbolic variable _C (introduced by the ODE solver) spoils the fun. Your attempt [g(x) for _C in srange(-8, 8, 0.4)] however creates just a list of copies of $g(x)$, without doing any substitution (that you intended). To do the subtitution, you can write e.g. [g(x).subs({var('_C') : _C}) for _C in srange(-8, 8, 0.4)]. Then it works:

As observed in the question, the solution contains a parameter _C.

That parameter does not get declared globally, so we need to do that before we can use it.

Here is one way using subs.

Define the variable, the function, the differential equation.

sage: x = SR.var('x')
sage: y = function('y')
sage: yprime = diff(y(x), x)
sage: de = (x^2)*yprime == y(x)
sage: de
x^2*diff(y(x), x) == y(x)

Solve.

sage: g(x) = desolve(de, [y(x), x])
sage: g
x |--> _C*e^(-1/x)

Declare the parameter as a symbolic variable.

sage: _C = SR.var('_C')

Plot solutions for a range of values of the parameter.

sage: dessin = plot([g(x).subs({_C: c}) for c in srange(-8, 8, 0.4)], (x, -3, 3))
sage: dessin.show(xmin=-1, xmax=1, ymin=-0.3, ymax=0.3)
Launched png viewer for Graphics object consisting of 80 graphics primitives