[Maxima-commits] CVS: maxima/share/contrib/diffequations/tests rtest_ode1_abel.mac,1.2,1.3

[David B. <bil...@us...>]

Update of /cvsroot/maxima/maxima/share/contrib/diffequations/tests
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv22428

Modified Files:
	rtest_ode1_abel.mac 
Log Message:
2004-05-04  David Billinghurst

	* share/contrib/diffequations/tests/rtest_ode1_abel.mac
	Update tests to reflect changes to ode1_abel.mac


Index: rtest_ode1_abel.mac
===================================================================
RCS file: /cvsroot/maxima/maxima/share/contrib/diffequations/tests/rtest_ode1_abel.mac,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -d -r1.2 -r1.3
--- rtest_ode1_abel.mac	3 May 2004 05:19:15 -0000	1.2
+++ rtest_ode1_abel.mac	4 May 2004 04:45:08 -0000	1.3
@@ -15,21 +15,19 @@
 (pn_(79),ans:ode1_abel(eqn:'diff(y,x)+(a*exp(x)+y)*y^2=0,y,x));
 false;
 
-/* about the simplest Abel equation - Case g.i*/
-/* This solves using ode1_abel_f0_0_f1_0 but not ode1_abel_absolute_invariant_constant */
+/* about the simplest Abel equation */
 ans:ode1_abel(eqn:'diff(y,x)=(x+c)*y^3+y^2,y,x);
--(sqrt(3)*log((x+c)^2*y^2+(x+c)*y+1)+2*atan((2*(x+c)*y+1)/sqrt(3))-2*sqrt(3)*log((x+c)*y))/(2*sqrt(3))=log(x+c)+%c;
-subst(y,y(x),diff(subst(y(x),y,ans),x));
+[-(sqrt(3)*log((x+c)^2*y^2+(x+c)*y+1)+2*atan((2*(x+c)*y+1)/sqrt(3))-2*sqrt(3)*log((x+c)*y))/(2*sqrt(3))=log(x+c)+%c];
+subst(y,y(x),diff(subst(y(x),y,ans[1]),x));
 -(sqrt(3)*(2*(x+c)^2*y*'diff(y,x,1)+(x+c)*'diff(y,x,1)+2*(x+c)*y^2+y)/((x+c)^2*y^2+(x+c)*y+1)+2*(2*(x+c)*'diff(y,x,1)+2*y)/(sqrt(3)*((2*(x+c)*y+1)^2/3+1))-2*sqrt(3)*((x+c)*'diff(y,x,1)+y)/((x+c)*y))/(2*sqrt(3))=1/(x+c);
 solve(%,'diff(y,x));
 ['diff(y,x,1) = (x+c)*y^3+y^2];
 lhs(eqn)-rhs(eqn),%;
 0;
 
-/* Tests for case g.i */
 ans:ode1_abel(eqn:'diff(y,x)=2*x^3*y^3+2*x*y^2,y,x);
--(sqrt(3)*log(x^4*y^2+x^2*y+1)+2*atan((2*x^2*y+1)/sqrt(3))-2*sqrt(3)*log(x^2*y))/(4*sqrt(3))=log(x)+%c;
-subst(y,y(x),diff(subst(y(x),y,ans),x));
+[-(sqrt(3)*log(x^4*y^2+x^2*y+1)+2*atan((2*x^2*y+1)/sqrt(3))-2*sqrt(3)*log(x^2*y))/(4*sqrt(3))=log(x)+%c];
+subst(y,y(x),diff(subst(y(x),y,ans[1]),x));
 -(sqrt(3)*(2*x^4*y*'diff(y,x,1)+x^2*'diff(y,x,1)+4*x^3*y^2+2*x*y)/(x^4*y^2+x^2*y+1)+2*(2*x^2*'diff(y,x,1)+4*x*y)/(sqrt(3)*((2*x^2*y+1)^2/3+1))-2*sqrt(3)*(x^2*'diff(y,x,1)+2*x*y)/(x^2*y))/(4*sqrt(3))=1/x;
 solve(%,'diff(y,x));
 ['diff(y,x,1) = 2*x^3*y^3+2*x*y^2];
@@ -40,23 +38,23 @@
    for f[0] for "random" f[1],f[2],f[3] 
 */
 ans:ode1_abel(eqn:'DIFF(y,x,1)=x*y^3+x*y^2+y+(9*x^2-2*x^3)/(27*x^2),y,x);
-y=%E^(x-x^2/6)/SQRT(%C-2*'INTEGRATE(x*%E^(2*(x-x^2/6)),x))-1/3;
-ode_check(eqn,ans);
+[y=%E^(x-x^2/6)/SQRT(%C-2*'INTEGRATE(x*%E^(2*(x-x^2/6)),x))-1/3];
+ode_check(eqn,ans[1]);
 0;
 
 ans:ode1_abel(eqn:'diff(y,x,1)=y^3/x+y,y,x);
-y=%e^x/sqrt(%c-2*'integrate(%e^(2*x)/x,x));
-ode_check(eqn,ans);
+[y=%e^x/sqrt(%c-2*'integrate(%e^(2*x)/x,x))];
+ode_check(eqn,ans[1]);
 0;
 
 ans:ode1_abel(eqn:'diff(y,x,1)=y^3+x^2*y,y,x);
-y=%e^(x^3/3)/sqrt(%c-2*'integrate(%e^(2*x^3/3),x));
-ode_check(eqn,ans);
+[y=%e^(x^3/3)/sqrt(%c-2*'integrate(%e^(2*x^3/3),x))];
+ode_check(eqn,ans[1]);
 0;
 
 ans:ode1_abel(eqn:'diff(y,x,1)=x^2*y^3+x*y,y,x);
-y=%e^(x^2/2)/sqrt(%c-2*(sqrt(%pi)*%i*erf(%i*x)/4+x*%e^x^2/2));
-ode_check(eqn,ans);
+[y=%e^(x^2/2)/sqrt(%c-2*(sqrt(%pi)*%i*erf(%i*x)/4+x*%e^x^2/2))];
+ode_check(eqn,ans[1]);
 0;
 
 /* Cheb-Terrab and Roche (31) */
@@ -90,9 +88,8 @@
 assume(b^2>0,(b^2+4*a)>0);
 [b^2>0,(b^2+4*a)>0];
 (kn_(41),ans:ode1_abel(eqn:'diff(y,x) + a*x*y^3 + b*y^2 ,y,x));
--(b*LOG(-(-2*a*x*y+SQRT(b^2+4*a)-b)/(2*a*x*y+SQRT(b^2+4*a)+b))+SQRT(b^2+4*a)*(LOG(a^2*x^2*y^2+a*b*x*y-a)-2*LOG(a*x*y/b)))/(2*SQRT(b^2+4*a))=LOG(x)+%C;
-
-subst(y,y(x),diff(subst(y(x),y,ans),x));
+[-(b*LOG(-(-2*a*x*y+SQRT(b^2+4*a)-b)/(2*a*x*y+SQRT(b^2+4*a)+b))+SQRT(b^2+4*a)*(LOG(a^2*x^2*y^2+a*b*x*y-a)-2*LOG(a*x*y/b)))/(2*SQRT(b^2+4*a))=LOG(x)+%C];
+subst(y,y(x),diff(subst(y(x),y,ans[1]),x));
 -(SQRT(b^2+4*a)*((2*a^2*x^2*y*'DIFF(y,x,1)+a*b*x*'DIFF(y,x,1)+2*a^2*x*y^2+a*b*y)/(a^2*x^2*y^2+a*b*x*y-a)-2*b*(a*x*'DIFF(y,x,1)/b+a*y/b)/(a*x*y))-b*(2*a*x*y+SQRT(b^2+4*a)+b)*((-2*a*x*y+SQRT(b^2+4*a)-b)*(2*a*x*'DIFF(y,x,1)+2*a*y)/(2*a*x*y+SQRT(b^2+4*a)+b)^2-(-2*a*x*'DIFF(y,x,1)-2*a*y)/(2*a*x*y+SQRT(b^2+4*a)+b))/(-2*a*x*y+SQRT(b^2+4*a)-b))/(2*SQRT(b^2+4*a))=1/x;
 solve(%,'diff(y,x));
 ['DIFF(y,x,1) = -a*x*y^3-b*y^2];
@@ -103,16 +100,16 @@
 
 /* Kamke 46  relative invariant = 0 */
 (kn_(46),a:1,ans:ode1_abel(eqn:'diff(y,x)- x^a*y^3+3*y^2-x^(-a)*y-x^(-2*a)+ a*x^(-a-1),y,x));
-y=1/x+1/(sqrt(1/x^2+%c)*x^2);
-ode_check(eqn,ans);
+[y=1/x+1/(sqrt(1/x^2+%c)*x^2)];
+ode_check(eqn,ans[1]);
 0;
 kill(a);
 done;
 assume(a>1);
 [a>1];
 (kn_(46),ans:ode1_abel(eqn:'diff(y,x)- x^a*y^3+3*y^2-x^(-a)*y-x^(-2*a)+ a*x^(-a-1),y,x));
-y=%e^-(2*x^(1-a)/(1-a))/sqrt(%c-2*'integrate(x^a*%e^-(4*x^(1-a)/(1-a)),x))+1/x^a;
-ode_check(eqn,ans);
+[y=%e^-(2*x^(1-a)/(1-a))/sqrt(%c-2*'integrate(x^a*%e^-(4*x^(1-a)/(1-a)),x))+1/x^a];
+ode_check(eqn,ans[1]);
 0;
 forget(a>1);
 [a>1];
@@ -132,8 +129,8 @@
 */
 (kn_(188),n:3,b:1,a:n+b,ans:ode1_abel(eqn:x^(2*n+1)*'diff(y,x)-a*y^3-b*x^(3*n),y,x));
 [LOG(-3*y/x^3-3)/3-LOG(3-6*y/x^3)/3+3/(3-6*y/x^3)-2*LOG(x)+LOG(-4/x^3)/3=%C];
-subst(y,y(x),diff(subst(y(x),y,ans),x));
-[(9*y/x^4-3*'DIFF(y,x,1)/x^3)/(3*(-3*y/x^3-3))-(18*y/x^4-6*'DIFF(y,x,1)/x^3)/(3*(3-6*y/x^3))-3*(18*y/x^4-6*'DIFF(y,x,1)/x^3)/(3-6*y/x^3)^2-3/x=0];
+subst(y,y(x),diff(subst(y(x),y,ans[1]),x));
+(9*y/x^4-3*'DIFF(y,x,1)/x^3)/(3*(-3*y/x^3-3))-(18*y/x^4-6*'DIFF(y,x,1)/x^3)/(3*(3-6*y/x^3))-3*(18*y/x^4-6*'DIFF(y,x,1)/x^3)/(3-6*y/x^3)^2-3/x=0;
 solve(%,'diff(y,x));
 ['DIFF(y,x,1) = (4*y^3+x^9)/x^7];
 eqn,%;
@@ -160,7 +157,7 @@
 
 /* Abel equations of second kind */
 (kn_(213),ans:contrib_ode(eqn:(y+1)*'DIFF(y,x)=y+x,y,x));
-[-(LOG((2*(x-1)/(y+1)-SQRT(5)+1)/(2*(x-1)/(y+1)+SQRT(5)+1))+SQRT(5)*LOG((x-1)/(y+1)+(x-1)^2/(y+1)^2-1)-2*SQRT(5)*LOG((x-1)/(y+1))/(2*SQRT(5))=LOG(x-1)+%C];
+[-(LOG((2*(x-1)/(y+1)-SQRT(5)+1)/(2*(x-1)/(y+1)+SQRT(5)+1))+SQRT(5)*LOG((x-1)/(y+1)+(x-1)^2/(y+1)^2-1)-2*SQRT(5)*LOG((x-1)/(y+1)))/(2*SQRT(5))=LOG(x-1)+%C];
 (dydx:subst(y,y(x),diff(subst(y(x),y,ans),x)),solve(dydx,'diff(y,x)));
 ['DIFF(y,x,1) = (y+x)/(y+1)];
 
@@ -194,4 +191,7 @@
 (dydx:subst(y,y(x),diff(subst(y(x),y,ans),x)),solve(dydx,'diff(y,x)));
 ['DIFF(y,x,1) = (x*y^2+x^3)/(2*y)];
 
-/* (kn_(221),ans:contrib_ode(eqn:(2*y+x+1)*'DIFF(y,x)-(2*y+x-1)=0,y,x));*/
+(kn_(221),ans:contrib_ode(eqn:(2*y+x+1)*'DIFF(y,x)-(2*y+x-1)=0,y,x));
+[-(2*y+x+1)*(-4*(2*(x+1)+2*(1-x))*LOG(1-(2*(x+1)+2*(1-x))/(3*(2*y+x+1)))/(3*(2*y+x+1))+4*(2*(x+1)+2*(1-x))*LOG(-(2*(x+1)+2*(1-x))/(3*(2*y+x+1)))/(3*(2*y+x+1))-4)/(3*(2*(x+1)+2*(1-x)))=x+%C];
+(dydx:subst(y,y(x),diff(subst(y(x),y,ans),x)),solve(dydx,'diff(y,x)));
+['DIFF(y,x,1)=(2*y+x-1)/(2*y+x+1)];