> restart;
> eq := diff(u(x, t), x, x)-(diff(u(x, t), t, t))/v^2 = 0;
print(`output redirected...`); # input placeholder
                                 d  / d         \
                                --- |--- u(x, t)|
          / d  / d         \\    dt \ dt        /
          |--- |--- u(x, t)|| - ----------------- = 0
          \ dx \ dx        //           2
                                       v
> phi1(x) := piecewise(0<=x and x<l-epsilon, 0, l-epsilon  <=x and x<=l, P/rho/epsilon/S);  ;
print(`output redirected...`); # input placeholder
                       /
         x -> piecewise|0 <= x and x < l - epsilon, 0,
                       \

                                              P      \
           l - epsilon <= x and x <= l, -------------|
                                        rho epsilon S/
> phi2(x) := 2*P/rho/S*Dirac(l-x);
print(`output redirected...`); # input placeholder
     2 P Dirac(l - x)
x -> ----------------
          rho S
> subs(u(x, t) = X(x)*T(t), eq); expand(lhs(%)/(X(x)*T(t))) = 0;
print(`output redirected...`); # input placeholder
               d  / d      \    d  / d      \
              --- |--- X(x)|   --- |--- T(t)|
               dx \ dx     /    dt \ dt     /
              -------------- - -------------- = 0
                   X(x)                 2
                                  T(t) v
> s1 := op(1, lhs(%)) = -lambda^2; s2 := op(2, lhs(`%%`)) = lambda^2;
print(`output redirected...`); # input placeholder
                    d  / d      \
                   --- |--- X(x)|
                    dx \ dx     /          2
                   -------------- = -lambda
                        X(x)
                      d  / d      \
                     --- |--- T(t)|
                      dt \ dt     /         2
                   - -------------- = lambda
                              2
                        T(t) v
> dsolve(s1, X(x));
print(`output redirected...`); # input placeholder
          X(x) = _C1 sin(lambda x) + _C2 cos(lambda x)
> subs(coeff(rhs(%), sin(lambda*x)) = A, coeff(rhs(%), cos(lambda*x)) = B, %);
print(`output redirected...`); # input placeholder
            X(x) = A sin(lambda x) + B cos(lambda x)
> X := unapply(rhs(%), x);
> {X(0) = 0, (D(X))(l) = 0};
print(`output redirected...`); # input placeholder
  {B = 0, A cos(lambda l) lambda - B sin(lambda l) lambda = 0}
> M := linalg[genmatrix](%, {A, B});
print(`output redirected...`); # input placeholder

> Delta := linalg[det](M);
print(`output redirected...`); # input placeholder
                     -cos(lambda l) lambda
> _EnvAllSolutions := true; solve(Delta = 0, lambda);
print(`output redirected...`); # input placeholder
                          Pi (1 + 2 _Z1)
                       0, --------------
                               2 l
> `minus`(indets(%[2]), {l});
%;
                             {_Z1}
> subs(%[1] = 'k', `%%`[2]); lambda := unapply(%, k);
print(`output redirected...`); # input placeholder
     Pi (1 + 2 k)
k -> ------------
         2 l
> X[k](x) := subs({lambda=lambda(k), B=0}, X(x));  ;