How to interpolate in terms of any form of algebra in maple?

For example, to interpolate a time series in terms of exponential or mixed with cos and sin?

r := 1;
c := 1;
G := 1;
M := 1;
theta := 90;

ex1 := {
Diff(f1(t), t$2)
+ 2*(-G*M/(r*(-r*c^2+2*G*M)))*Diff(f(t), t1)*Diff(f2(t), t) = 0,

Diff(f2(t), t$2)
+ (-(-r*c^2+2*G*M)*G*M/(r^3*c^4))*Diff(f1(t), t)^2
+ (G*M/(r*(-r*c^2+2*G*M)))*Diff(f2(t), t$2)
+ ((-r*c^2+2*G*M)/c^2)*Diff(f3(t), t$2)
+ ((-r*c^2+2*G*M)*sin(theta)^2/c^2)*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)
+ (-sin(theta)*cos(theta))*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)

How to solve a set or a system of differential equations in maple for motion with Schwarzchild metric?

************** Schwarzchild metric *****************
with(tensor):
coord := [t, r, theta, Phi]:

g_compts:=array(symmetric,sparse,1..4,1..4):

g_compts[1,1]:=1 - 2*G*M/(r*c^2):
g_compts[2,2]:=-(1 - 2*G*M/(r*c^2))^(-1):
g_compts[3,3]:=-r^2:
g_compts[4,4]:=-(r^2)*sin(theta)^2:

g1 := create([-1,-1], eval(g_compts)):

alpha := vector([cos(theta), sin(theta), sin(k*theta)]);

alpha1 := map(diff, alpha, theta);
alpha11 := map(diff, alpha1, theta);

with(linalg):
cr := multiply(alpha1, alpha11)/simplify(multiply(alpha1, alpha1));

F := vector([0, 0, -m*g]);
c := multiply(F, alpha1/simplify(multiply(alpha1, alpha1)))/m;

motion := diff(f(theta), theta$2) + cr*diff(f(theta), theta)^2 = c;

pdsolve and dsolve not work, how to solve above motion equation with maple?

g(theta) := array([[cos(theta), -sin(theta)],[sin(theta), cos(theta)]]);
dg := map(diff, g(theta), theta);
invg := inverse(g(theta));
w := multiply(invg, dg);
w := map(simplify, w);

crossprod(-w, w); <- have error?

How to cross product between matrix?

As i know wedge product is cross product, so i use cross product