Hi everybody,
To become familiar with ODEs with Sage, I am trying to solve a very
simple ODE with the Laplace method implemented in Sage
In concrete, i want to solve
dy(t)/dt = -k*y(t)
with for example, initial conditions y(0)=1
For that:
>>> t = var('t')
>>> k = var('k')
>>> y = function('y',t)
>>> myODE = diff(y,t)+k*y==0
>>> mysol = desolve_laplace(de=myODE, ivar=t, dvar=y, ics=[1,0])
mysol gets the value:
>>> e^(-k*t)*y(0)
Works fine, but I am not able to set the initial condition y(0) to 1.
The documentation say that the argument "ics" is a list of numbers which
correspond the solution to the function when the independent value is
zero. Am i missing something???
I would like to obtain the solution in the form
>> mysol(t) = e^(-k*t)
So that I can plot the solution with different values of k
>>> fig1 = plot(mysol.subs(k=1/5.), 0, 10)
>>> fig2 = plot(mysol.subs(k=1/2.), 0, 10)
Of course, for more complex ODEs
Thanks a lot in advance.
Nin
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