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Viewing changes to share/contrib/diffequations/tests/rtest_ode1_abel.mac

  • Committer: Bazaar Package Importer
  • Author(s): Camm Maguire
  • Date: 2006-10-18 14:52:42 UTC
  • mto: (1.1.5 upstream)
  • mto: This revision was merged to the branch mainline in revision 4.
  • Revision ID: james.westby@ubuntu.com-20061018145242-vzyrm5hmxr8kiosf
Import upstream version 5.10.0

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share/contrib/diffequations/tests/rtest_ode1_abel.mac
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/* Murphy 78 Abel */
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(pn_(78),ans:ode1_abel(eqn:'diff(y,x)+(a*x+y)*y^2=0,y,x));
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false;
 
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[];
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/* Murphy 79 Abel */
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(pn_(79),ans:ode1_abel(eqn:'diff(y,x)+(a*exp(x)+y)*y^2=0,y,x));
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false;
 
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[];
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/* about the simplest Abel equation */
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ans:ode1_abel(eqn:'diff(y,x)=(x+c)*y^3+y^2,y,x);
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/* and now some cases with relative invariant = 0.  All generated by solving 
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   for f[0] for "random" f[1],f[2],f[3] 
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*/
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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);
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[y=%E^(x-x^2/6)/SQRT(%C-2*'INTEGRATE(x*%E^(2*(x-x^2/6)),x))-1/3];
 
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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);
 
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[y=%e^(x-x^2/6)/sqrt(%c-2*'integrate(x*%e^(2*(x-x^2/6)),x))-1/3];
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ode_check(eqn,ans[1]);
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0;
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/* Cheb-Terrab and Roche (31) */
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ans:ode1_abel(eqn:'diff(y,x)=y^3/x+y^2,y,x);
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false;
 
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[];
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/* Cheb-Terrab and Roche (33) */
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ans:ode1_abel(eqn:'diff(y,x)=(x+1/x+1/x^3)*y^3/x+y^2,y,x);
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false;
 
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[];
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/* According to Cheb-Terrab and Roche, the following 
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   equations from kamke have constant invariant */
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*/
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(kn_(38),a:-1/6,b:1/3,ans:ode1_abel(eqn:'diff(y,x) - a*y^3 - b*x^(-3/2),y,x));
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 [-LOG(3*SQRT(x)*y+3)/3+LOG(3*SQRT(x)*y/2-3)/3+3/(3*SQRT(x)*y+3)+3*LOG(x)/2+LOG(1/(54*x^3))/3=%C];
 
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[-log(3*sqrt(x)*y+3)/3+log(3*sqrt(x)*y/2-3)/3+3/(3*sqrt(x)*y+3)+3*log(x)/2+log(1/(54*x^3))/3=%c];
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[method,ode_check(eqn,ans[1])];
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[abel,0];
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kill(a,b);
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assume(b^2>0,(b^2+4*a)>0);
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[b^2>0,(b^2+4*a)>0];
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(kn_(41),ans:ode1_abel(eqn:'diff(y,x) + a*x*y^3 + b*y^2 ,y,x));
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[-(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];
 
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[-(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];
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[method,ode_check(eqn,ans[1])];
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[abel,0];
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forget(b^2>0,(b^2+4*a)>0);
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    (n:7, b:2, a:n+b);   => K = -343/36
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*/
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(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));
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[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];
 
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[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];
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[method,ode_check(eqn,ans[1])];
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[abel,0];
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kill(a,b,n);
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/* Non-constant invariant */
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(kn_(36),ans:ode1_abel(eqn:'diff(y,x)+y^3+a*x*y^2,y,x));
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false;
 
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[];
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(kn_(37),ans:ode1_abel(eqn:'diff(y,x)-y^3-a*exp(x)*y^2,y,x));
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false;
 
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[];
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(kn_(40),ans:ode1_abel(eqn:'diff(y,x)+3*a*y^3+6*a*x*y^2,y,x));
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false;
 
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[];
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(kn_(42),ans:ode1_abel(eqn:'diff(y,x)-x*(x+2)*y^3-(x+3)*y^2,y,x));
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false;
 
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[];
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(kn_(43),ans:ode1_abel(eqn:'diff(y,x)+(3*a*x^2+4*a^2*x+b)*y^3+3*x*y^2,y,x));
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false;
 
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[];
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(kn_(45),ans:ode1_abel(eqn:'diff(y,x)+2*(a^2*x^3-b^2*x)*y^3+3*b*y^2,y,x));
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false;
 
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[];
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/* Abel equations of second kind */
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(kn_(213),ans:ode1_abel(eqn:(y+1)*'DIFF(y,x)=y+x,y,x));
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[-(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];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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(kn_(214),ans:ode1_abel(eqn:(y+x-1)*'DIFF(y,x)-y+2*x+3=0,y,x));
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[-(2*ATAN((1-(3*x+2)/(y+x-1))/SQRT(2))+SQRT(2)*LOG(-2*(3*x+2)/(y+x-1)+(3*x+2)^2/(y+x-1)^2+3)-2*SQRT(2)*LOG(-(3*x+2)/(2*(y+x-1))))/(6*SQRT(2))=LOG(3*x+2)/3+%C];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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(kn_(215),ans:ode1_abel(eqn:(y+2*x-2)*'DIFF(y,x)-y+x+1=0,y,x));
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[-(6*ATAN((3-2*(3*x-1)/(y+2*x-2))/SQRT(3))+SQRT(3)*LOG(-(3*x-1)/(y+2*x-2)+(3*x-1)^2/(3*(y+2*x-2)^2)+1)-2*SQRT(3)*LOG(-(3*x-1)/(3*(y+2*x-2))))/(6*SQRT(3))=LOG(3*x-1)/3+%C];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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(kn_(216),ans:ode1_abel(eqn:(y-2*x+1)*'DIFF(y,x)+y+x=0,y,x));
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[-(6*ATAN((2*(3*x-1)/(y-2*x+1)+3)/SQRT(3))+SQRT(3)*LOG((3*x-1)/(y-2*x+1)+(3*x-1)^2/(3*(y-2*x+1)^2)+1)-2*SQRT(3)*LOG((3*x-1)/(3*(y-2*x+1))))/(6*SQRT(3))=LOG(3*x-1)/3+%C];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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(kn_(217),ans:ode1_abel(eqn:(y-x^2)*'DIFF(y,x)=x,y,x));
 
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(kn_(213),ans:ode1_abel(eqn:(y+1)*'diff(y,x)=y+x,y,x));
 
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[-(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];
 
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[method,ode_check(eqn,ans[1])];
 
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[abel2,0];
 
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(kn_(214),ans:ode1_abel(eqn:(y+x-1)*'diff(y,x)-y+2*x+3=0,y,x));
 
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[-(2*atan((1-(3*x+2)/(y+x-1))/sqrt(2))+sqrt(2)*log(-2*(3*x+2)/(y+x-1)+(3*x+2)^2/(y+x-1)^2+3)-2*sqrt(2)*log(-(3*x+2)/(2*(y+x-1))))/(6*sqrt(2))=log(3*x+2)/3+%c];
 
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[method,ode_check(eqn,ans[1])];
 
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[abel2,0];
 
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(kn_(215),ans:ode1_abel(eqn:(y+2*x-2)*'diff(y,x)-y+x+1=0,y,x));
 
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[-(6*atan((3-2*(3*x-1)/(y+2*x-2))/sqrt(3))+sqrt(3)*log(-(3*x-1)/(y+2*x-2)+(3*x-1)^2/(3*(y+2*x-2)^2)+1)-2*sqrt(3)*log(-(3*x-1)/(3*(y+2*x-2))))/(6*sqrt(3))=log(3*x-1)/3+%c];
 
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[method,ode_check(eqn,ans[1])];
 
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[abel2,0];
 
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(kn_(216),ans:ode1_abel(eqn:(y-2*x+1)*'diff(y,x)+y+x=0,y,x));
 
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[-(6*atan((2*(3*x-1)/(y-2*x+1)+3)/sqrt(3))+sqrt(3)*log((3*x-1)/(y-2*x+1)+(3*x-1)^2/(3*(y-2*x+1)^2)+1)-2*sqrt(3)*log((3*x-1)/(3*(y-2*x+1))))/(6*sqrt(3))=log(3*x-1)/3+%c];
 
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[method,ode_check(eqn,ans[1])];
 
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[abel2,0];
 
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(kn_(217),ans:ode1_abel(eqn:(y-x^2)*'diff(y,x)=x,y,x));
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[(y-x^2)*(log(-1/(2*(y-x^2)))/(2*(y-x^2))-log(1-1/(2*(y-x^2)))/(2*(y-x^2))-1)/2= x^2/2+%c];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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(kn_(218),ans:ode1_abel(eqn:(y-x^2)*'DIFF(y,x)+4*x*y=0,y,x));
 
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(kn_(218),ans:ode1_abel(eqn:(y-x^2)*'diff(y,x)+4*x*y=0,y,x));
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[(log(2*x^2/(y-x^2)+2)-2*log(2*x^2/(y-x^2)+1)+log(2*x^2/(3*(y-x^2))))/2=log(x)+%c];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];
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/* Why does this fail? */
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/* (kn_(220),ans:ode1_abel(eqn:2*y*'DIFF(y,x)-x*y^2-x^3=0,y,x));
171
 
[%E^-(x^2/2)*(y^2+x^2+2) = %C];
 
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/* (kn_(220),ans:ode1_abel(eqn:2*y*'diff(y,x)-x*y^2-x^3=0,y,x));
 
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[%e^-(x^2/2)*(y^2+x^2+2) = %c];
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[method,ode_check(eqn,ans[1])];
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[abel2,0]; */
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(kn_(221),ans:ode1_abel(eqn:(2*y+x+1)*'DIFF(y,x)-(2*y+x-1)=0,y,x));
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[-(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];
 
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(kn_(221),ans:ode1_abel(eqn:(2*y+x+1)*'diff(y,x)-(2*y+x-1)=0,y,x));
 
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[-(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];
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[method,ode_check(eqn,ans[1])];
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[abel2,0];