1 | initial version |
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))
2 | No.2 Revision |
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)
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