% kamken3o.tst: Kamke Nonlinear order>=3 ODE examples  -*- REDUCE -*-

% F.J.Wright@Maths.QMW.ac.uk, 21 May 1996

% Taken from ``Differentialgleichungen: Loesungsmethoden und
% Loesungen'', E. Kamke, Vol. 1: Gewoehnliche Differentialgleichungen,
% second edition, Akademische Verlagsgesellschaft, Leipzig, 1943.

% The format of the examples is intended to be as close as possible to
% that printed in the book.

% Part C. Einzel-Differentialgleichungen, Section 7: Nichtlineare
% Differentialgleichungen dritter und hoeherer Ordnung, pp.600--605.

depend y, x;

% 7.1
odesolve(df(y,x,3) = a^2*(df(y,x)^5 + 2df(y,x)^3 + df(y,x)), y, x);

% 7.2
odesolve(df(y,x,3) + y*df(y,x,2) - df(y,x)^2 + 1 = 0, y, x);

% 7.3
odesolve(df(y,x,3) - y*df(y,x,2) + df(y,x)^2 = 0, y, x);

% 7.4
odesolve(df(y,x,3) + a*y*df(y,x,2) = 0, y, x);

% 7.5
operator f;
odesolve(x^2*df(y,x,3) + x*df(y,x,2) + (2x*y-1)*df(y,x) + y^2 = f(x),
   y, x);

% 7.6
odesolve(x^2*df(y,x,3) + x*(y-1)*df(y,x,2) + x*df(y,x)^2 +
   (1-y)*df(y,x) = 0, y, x);

% 7.7
odesolve(y*df(y,x,3) - df(y,x)*df(y,x,2) + y^3*df(y,x) = 0, y, x);

% 7.8
odesolve(4y^2*df(y,x,3) - 18y*df(y,x)*df(y,x,2) + 15df(y,x)^3 = 0,
   y, x);

% 7.9
odesolve(9y^2*df(y,x,3) - 45y*df(y,x)*df(y,x,2) + 40df(y,x)^3 = 0,
   y, x);

% 7.10
odesolve(2df(y,x)*df(y,x,3) - 3df(y,x,2)^2 = 0, y, x);

% 7.11
odesolve((df(y,x)^2+1)*df(y,x,3) - 3df(y,x)*df(y,x,2)^2 = 0, y, x);

% 7.12
odesolve((df(y,x)^2+1)*df(y,x,3) - (3df(y,x)+a)*df(y,x,2)^2 = 0,
   y, x);

% 7.13
odesolve(df(y,x,2)*df(y,x,3) = a*sqrt(b^2*df(y,x,2)^2+1) = 0, y, x);

% 7.14
odesolve(df(y,x)*df(y,x,4) - df(y,x,2)*df(y,x,3) +
   df(y,x)^3*df(y,x,3) = 0, y, x);

% 7.15
depend {f,g}, x;
y!' := df(y,x)$  y!" := df(y,x,2)$
odesolve(y!'*df(f*y!',x,3) - y!"*df(f*y!',x,2) + y!'^3*df(f*y!',x) +
   2g*y!'^2*sin y + (g*y!"-df(g,x)*y!')*cos y = 0, y, x);

% 7.16
odesolve(3df(y,x,2)*df(y,x,4) - 5df(y,x,3)^2 = 0, y, x);

% 7.17
odesolve(9df(y,x,2)^2*df(y,x,5) - 45df(y,x,2)*df(y,x,3)*df(y,x,4) +
   40df(y,x,3)^3 = 0, y, x);

% 7.18
%% odesolve(df(y,x,n) = f(df(y,x,n-1)), y, x);
%% No standard syntax for symbolic n'th order derivatives!

% 7.19
%% odesolve(df(y,x,n) = f(df(y,x,n-2)), y, x);
%% No standard syntax for symbolic n'th order derivatives!

end;