/*************** -*- Mode: MACSYMA; Package: MAXIMA -*-  ******************/
/***************************************************************************
***                                                                    *****
***     Copyright (c) 1984 by William Schelter,University of Texas     *****
***     All rights reserved                                            *****
***************************************************************************/

kill(all);
done;
x^2*'diff(y,x,1)+3*x*y = sin(x)/x;
x^2*'diff(y,x,1)+3*x*y = sin(x)/x$
soln1:ode2(%,y,x);
y = (%c-cos(x))/x^3$
ic1(soln1,x = %pi,y = 0);
y = -((cos(x)+1)/x^3)$
'diff(y,x,2)+y*('diff(y,x,1))^3 = 0;
'diff(y,x,2)+y*('diff(y,x,1))^3 = 0$
soln2:ode2(%,y,x);
(y^3+6*%k1*y)/6 = x+%k2$

bc2(soln2,x = 0,y = 1,x = 1,y = 3);
(y^3-10*y)/6 = x-3/2$
exp:k^2*n^2+k^2*m^2*n^2-k^2*l^2*n^2-k^2*l^2*m^2*n^2;
-k^2*l^2*m^2*n^2+k^2*m^2*n^2-k^2*l^2*n^2+k^2*n^2$
eq1:k^2+l^2 = 1;
l^2+k^2 = 1$
eq2:n^2-m^2 = 1;
n^2-m^2 = 1$
scsimp(exp,eq1,eq2);
k^4*n^4$
exq:(k1*k4-k1*k2-k2*k3)/k3^2;
(k1*k4-k2*k3-k1*k2)/k3^2$
eq3:k1*k4-k2*k3 = 0;
k1*k4-k2*k3 = 0$
eq4:k1*k2+k3*k4 = 0;
k3*k4+k1*k2 = 0$
scsimp(exq,eq3,eq4);
k4/k3$
exp1:2*x^2+y*x+z;
z+x*y+2*x^2$
exp2:3*x+5*y-z-1;
-z+5*y+3*x-1$
exp3:z^2+x-y^2+5;
z^2-y^2+x+5$
eliminate([exp3,exp2,exp1],[y,z]);
[7425*x^8-1170*x^7+1299*x^6+12076*x^5+22887*x^4-5154*x^3-1291*x^2+7688*x+15376]$
eqn1:'diff(f(x),x) = 'diff(g(x),x)+sin(x);
'diff(f(x),x,1) = 'diff(g(x),x,1)+sin(x)$
eqn2:'diff(g(x),x,2) = 'diff(f(x),x)-cos(x);
'diff(g(x),x,2) = 'diff(f(x),x,1)-cos(x)$
atvalue('diff(g(x),x),x = 0,a);
a$
atvalue(f(x),x = 0,1);
1$