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bc2-cos-diff-ode2-plot2d-rhs
plot2d(rhs(eqnend),[x,-1,2],[xlabel,"x"],[ylabel,"y(x)"]);

eqn:'diff(y,x,2)-3*'d...

sol:ode2(eqn,y,x);

eqnend:bc2(sol,x=-1,y...

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+y*cos(...

x1:0;

x2:2;

Calculate

bc2-cos-diff-ode2-plot2d-rhs
plot2d(rhs(solc),[x,-1,1]);

F:(Dy)^2 + 4*(y)^2 + ...

Fy:diff(F,y);

Fdy:diff(F,Dy);

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
 plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+y*cos(...

x1:0;

x2:2;

Calculate

bc2-cos-diff-ode2-plot2d-rhs
plot2d(rhs(sol1),[x,-4,0],[xlabel,"x"],[ylabel,"y(x)"]);

eqn4:diff(y(x),x,2)+d...

sol:ode2(eqn4,y,x);

sol1:bc2(sol,x=-4,y=1...

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
 plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+y*cos(...

x1:0;

x2:2;

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+y*cos(...

x1:0;

x2:2;

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
plot2d(rhs(eq),[x,-1,1],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+3*y*%e...

dF:diff(F,Dy);

eqn:diff(F,y)-diff(dF...

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:2*Dy^2+2*y^2+y*cos(...

x1:0;

x2:2;

Calculate

bc2-cos-diff-ode2-plot2d-rhs
plot2d(rhs(solc),[x,-1,1]);

F:(Dy)^2 + 4*(y)^2 + ...

Fy:diff(F,y);

Fdy:diff(F,Dy);

Calculate

[bc2,cos,diff,ode2,plot2d,rhs]

Run Example
(%i1)eqn4:diff(y(x),x,2)+diff(y(x),x)=cos(x);
                         2
                        d            d
(%o1)                   --- (y(x)) + -- (y(x)) = cos(x)
                          2          dx
                        dx
(%i2) sol:ode2(eqn4,y,x);
                         2
                        d            d
(%t2)                   --- (y(x)) + -- (y(x)) = cos(x)
                          2          dx
                        dx

                                     msg1

(%o2)                                false
(%i3) sol1:bc2(sol,x=-4,y=1,x=0,y=0);
(%o3)                                 []
(%i4) plot2d(rhs(sol1),[x,-4,0],[xlabel,"x"],[ylabel,"y(x)"]);
plotplot2d(rhs(sol1),[x,-4,0],[xlabel,"x"],[ylabel,"y(x)"]);
Run Example
F:(Dy)^2 + 4*(y)^2 + 4*(x^2)*y + x*cos(x);
                           2      2                  2
(%o1)                   4 y  + 4 x  y + x cos(x) + Dy
(%i2) Fy:diff(F,y);
                                           2
(%o2)                             8 y + 4 x
(%i3) Fdy:diff(F,Dy);
(%o3)                                2 Dy
(%i4) dfdy:2*'diff(Fdy,x);
                                    d
(%o4)                            2 (-- (2 Dy))
                                    dx
(%i5) eqn:Fy-dfdy=0;
                                 2      d
(%o5)                   8 y + 4 x  - 2 (-- (2 Dy)) = 0
                                        dx
(%i6) sol:ode2(eqn,y,x);
                                 2      d
(%t6)                   8 y + 4 x  - 2 (-- (2 Dy)) = 0
                                        dx

                                     msg1

(%o6)                                false
(%i7) solc:bc2(sol,x=-1,y=2, x=1,y=1/2);
(%o7)                                 []
(%i8) plot2d(rhs(solc),[x,-1,1]);
plotplot2d(rhs(solc),[x,-1,1]);
Run Example
F:(Dy)^2 + 4*(y)^2 + 4*(x^2)*y + x*cos(x);
                           2      2                  2
(%o1)                   4 y  + 4 x  y + x cos(x) + Dy
(%i2) Fy:diff(F,y);
                                           2
(%o2)                             8 y + 4 x
(%i3) Fdy:diff(F,Dy);
(%o3)                                2 Dy
(%i4) dfdy:2*'diff(y,x,2);
                                        2
                                       d y
(%o4)                                2 ---
                                         2
                                       dx
(%i5) eqn:Fy-dfdy=0;
                                2
                               d y            2
(%o5)                      - 2 --- + 8 y + 4 x  = 0
                                 2
                               dx
(%i6) sol:ode2(eqn,y,x);
                                                     2
                              2 x         - 2 x   2 x  + 1
(%o6)               y = %k1 %e    + %k2 %e      - --------
                                                     4
(%i7) solc:bc2(sol,x=-1,y=2, x=1,y=1/2);
                6        2    2 x         6       2    - 2 x      2
           (5 %e  - 11 %e ) %e      (11 %e  - 5 %e ) %e        2 x  + 1
(%o7)  y = ---------------------- + ------------------------ - --------
                     8                         8                  4
                 4 %e  - 4                 4 %e  - 4
(%i8) plot2d(rhs(solc),[x,-1,1]);
plotplot2d(rhs(solc),[x,-1,1]);
[atan,cos,diff,kill,matrix,phi,plot2d,plot3d,ratsimp,rhs,sin,solve,sqrt,subst] [atvalue,bc2,desolve,diff,exp,ic2,ode2,plot2d,rhs,sin] [atvalue,bc2,diff,ode2,plot2d,rhs] [bc2,cos,diff,exp,length,makelist,ode2,plot2d,rhs,rk,sin,solve,subst] [bc2,cos,diff,numer,ode2,plot2d,rhs,solve,subst] [bc2,cos,diff,ode2,plot2d,rhs,subst] [bc2,cos,diff,ode2,plot2d,rhs] [bc2,dependencies,depends,diff,kill,ode2] [bc2,depends,diff,kill,ode2] [bc2,diff,exp,ode2,plot2d,rhs,solve,subst] [bc2,diff,first,ode2,plot2d,rhs,second,solve,subst] [bc2,diff,numer,ode2,plot2d,rhs,solve,subst] [bc2,diff,ode2,plot2d,rhs] [bc2,diff,ode2] [cos,define,diff,expand,find_root,float,log,plot2d] [cos,define,diff,expand,float,log,plot2d] [cos,define,diff,find_root,float,plot2d,sqrt] [cos,define,diff,float,plot2d,sqrt] [cos,diff,ev,find_root,plot2d] [cos,diff,float,ic2,ode2,plot2d,rhs,sin,sqrt] [cos,diff,float,ic2,ode2,plot2d,rhs,sqrt] [cos,diff,ic1,ode2,plot2d,rhs] [cos,diff,ic2,ode2,plot2d,rhs,sqrt] [cos,diff,ic2,ode2,plot2d,rhs] [cos,diff,integrate,load,plot2d,plot3d,sin] [cos,diff,integrate,plot2d,sin] [cos,diff,log,plot2d,sin] [cos,diff,numer,plot2d,sin,subst] [cos,diff,ode2,plot2d,rhs,sin,solve,subst] [cos,diff,ode2,plot2d,rhs] [cos,diff,ode2,sin,solve,sqrt] [cos,diff,ode2,sin] [cos,diff,ode2] [cos,diff,plot2d,sin,sqrt] [cos,diff,plot2d,sin,subst] [cos,diff,plot2d,sin] [cos,diff,plot2d,sqrt] [cos,diff,plot2d] [diff,disp,ic1,ode2,print,rhs] [diff,exp,ic2,ode2,plot2d,rhs] [diff,exp,ic2,ode2,plot2d] [diff,exp,integrate,ode2,plot2d] [diff,false,ic1,ode2,plot2d,ratprint,ratsimp,rhs] [diff,false,ic1,ode2,plot2d,ratprint,remvalue,rhs] [diff,ic1,ode2,plot2d,rhs,solve] [diff,ic1,ode2,plot2d,rhs] [diff,ic1,ode2,plot2d] [diff,ic2,ode2,plot2d,rhs] [diff,ode2,plot2d,rhs] [diff,ode2,plot2d]

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