read `HDequation.txt`:

N:=40:

gu:=HDniceS(N,b):

print(`Consider the Harry Dym Equation for u=u(x,t), u_t=u^3 u_xxx, with initial conditions u(0,t)=1, u_x(0,t)=a[1](t), u_xx(0,t)=a[2](t) `):
print(``):
print(`The first`, N+1,  `coefficients of the powers of x^i in the series expansion of the general solution (as a power series in x), in terms of the intial conditions, starting at i=0`):
print(``):
print(`where we use the abbreviation b[i,r]=d^r/dt^r a[i](t), for i=1,2 (or in maple b[i,r]=diff(a[i],t$r) are `):
print(``):
for i from 0 to N do
 print(`The coefficient of`, x^i, `is `):
 print(``):
 lprint(gu[i+1]):
 print(``):
od:

print(``):
print(`--------------------------`):
print(``):
print(`This took`, time(), `secdons. `):

quit: