On 16/06/11 13:32, David Joyner wrote:
On Thu, Jun 16, 2011 at 5:58 AM, Nin<[email protected]> wrote:
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
You meant
sage: t = var('t')
sage: k = var('k')
sage: y = function('y',t)
sage: myODE = diff(y,t)+k*y==0
sage: desolve_laplace(de=myODE, ivar=t, dvar=y, ics=[0,1])
e^(-k*t)
You can type type desolve_laplace? for more details on the syntax.
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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Fantastic, obviously I misunderstood the ics argument!
Thanks David!
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