Hello,
I am attempting to solve a system of four, coupled, linear ordinary
differential equations for which I know the initial starting
conditions. Unfortunately, I am unable to enter the system into
FriCAS, with the initial conditions. More generally, I can not seem
to solve any linear system of ODEs w/initial conditions:
y := operator 'y
x := operator 'x
eq1 := D(y t, t) = x(t)
eq2 := D(x t, t) = -y(t)
solve([eq1,eq2], [x,y], t=0,[x(0)=1,y(0)=0])
>> There are 2 exposed and 1 unexposed library operations named solve
having 4 argument(s) but none was determined to be applicable.
If I remove the list of initial conditions solve works. Additionally,
if I use seriesSolve, it also works. Can someone offer me the correct
syntax/cast to solve such a system in FriCAS? (The manual only covers
systems w/initial conditions with seriesSolve.)
Moving on I went ahead and tried to solve the system in Mathematica;
it got nowhere. Maxima, however, did give me a solution in terms of a
moderately complicated inverse laplace transform (which it could not
compute). Luckily, both FriCAS and Mathematica were happy to solve
it. FriCAS, like Mathematica gave a solution which had ROOT objects
and both %%A0 and %%A1:
subst(inverseLaplace((R*g2849^3+(G*R+G)*g2849^2+(R^2+R
+G^2)*g2849+2*G*R)/(10*(R*g2849^4+(G*R
+G)*g2849^3+subst(inverseLaplace((R*g2849^3+(G*R+G)*g2849^2+(R^2+R
+G^2)*g2849+2*G*R)/(10*(R*g2849^4+(G*R+G)*g2849^3+(2*R^2+2*R
+G^2)*g2849^2+(3*G*R+G)*g2849+R^2+R)),g2849,t), [G=2,R=100])
(The subst is done to clean up the equation somewhat, as I am only
interested in a few particular values of R and G.) My question is how
can I expand and solve the roots; eliminating them and %%A0 and %%A1.
Mathematica has a ToRadicals function (which successfully eliminates
all such roots). Once fully simplified the expression should be
representable in terms of decaying exponentials and trigonometric
functions.
Regards, Freddie.
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