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bc2-diff-ic2-ode2

Sol: ode2('diff(y,x,2...

ic2(Sol,x=0,y=0,'diff...

bc2(Sol,x=0,y=0,x=5,y...

Calculate

bc2-depends-diff-integrate-kill-ode2-rhs-solve-subst

kill(all);

depends(f,[x,y]);

depends(g,[x,y]);

Calculate

bc2-cos-diff-exp-ode2-sin

J: ('diff(y,x))^2+4*(...

eqn: diff(J,'diff(y,x...

sol: ode2(eqn,y,x);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-ode2

eqn:'diff(y,x,2)+y=0;

sol:ode2(eqn,y,x);

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

Calculate

bc2-diff-exp-ode2-plot2d-rhs-sin-solve-subst
plot2d(rhs(total), [x, x1, x2],[xlabel,"x"],[ylabel,"y(x)"]);

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

Fy: diff(F, y(x));

Fdy: diff(F, Dy(x));

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-numer-ode2-plot2d-rhs-solve-subst
plot2d([rhs(lab2), rhs(lab3), rhs(lab4)], [x,x1,x2], [xlabel,"x"], [ylabel,"y(x)"], [color, red, green, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

Psi:2*y1^2-y1*y2+3*y2...

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

x1:-1;

Calculate

bc2-cos-diff-numer-ode2-plot2d-rhs-solve-subst
plot2d([rhs(lab2), rhs(lab3), rhs(lab4)], [x,x1,x2], [xlabel,"x"], [ylabel,"y(x)"], [color, red, green, yellow], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

Psi:y2^2+y2;

F:Dy^2+4*y^2+4*x^2*y+...

x1:-1;

Calculate

bc2-diff-ode2-plot2d-rhs-solve-subst
plot2d([rhs(lab2), rhs(lab3), rhs(lab4)], [x,x1,x2], [xlabel,"x"], [ylabel,"y(x)"], [color, red, green, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

T:2*y1^2-y1*y2+3*y2^2...

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

x1:-1;

Calculate

bc2

Run Example
(%i1)eq:'diff(y,x)  = -xy +2*x;
                                 dy
(%o1)                            -- = 2 x - xy
                                 dx
(%i2) sol: ode2(eq,y,x);
                                           2
(%o2)                        y = - x xy + x  + %c
(%i3) ic1(sol, x= 0, y= 0);
                                      2
(%o3)                            y = x  - x xy
(%i4) eq1:(1+x^2)*'diff(y,x)+4*x*y=0;
                              2      dy
(%o4)                       (x  + 1) -- + 4 x y = 0
                                     dx
(%i5) sol1:ode2(eq1,y,x);
                                        %c
(%o5)                            y = ---------
                                       2     2
                                     (x  + 1)
(%i6) eq2: 'diff(y,x,2) + 'diff(y,x)-2*y = 0;
                               2
                              d y   dy
(%o6)                         --- + -- - 2 y = 0
                                2   dx
                              dx
(%i7) sol2:ode2(eq2,y,x);
                                     x         - 2 x
(%o7)                      y = %k1 %e  + %k2 %e
(%i8) bc2(sol2,x=0,y=0,x=0,y=1);
(%o8)                                 []
(%i9) 
Run Example
kill(all);
(%o0)                                done
(%i1) depends(f,[x,y]);
(%o1)                              [f(x, y)]
(%i2) depends(y,x);
(%o2)                               [y(x)]
(%i3) f(x,y):=12*x*y+(diff(y,x))^2;
                                                2
(%o3)                   f(x, y) := 12 x y + diff (y, x)
(%i4) l1:diff(f(x,y),y);
(%o4)                                12 x
(%i5) l2:diff(f(x,y),'diff(y,x));
                                       dy
(%o5)                                2 --
                                       dx
(%i6) l3:diff(l2,x);
                                        2
                                       d y
(%o6)                                2 ---
                                         2
                                       dx
(%i7) y1:ode2(l1-l3=0,y,x);
                                  3
(%o7)                        y = x  + %k2 x + %k1
(%i8) bc2(%,x=0,y=3,x=1,y=6);
(%o8)                                 []
(%i9) 
Run Example
eqn1: diff(y(x),x)=z;
                                 d
(%o1)                            -- (y(x)) = z
                                 dx
(%i2) eqn2: diff(z(x),x)=3*z - 2*y + exp^x;
                         d              x
(%o2)                    -- (z(x)) = exp  + 3 z - 2 y
                         dx
(%i3)  atvalue(y(x),x=0,2);
(%o3)                                  2
(%i4)  atvalue(z(x),x=0,3);
(%o4)                                  3
(%i5) result:desolve([eqn1,eqn2],[y(x),z(x)]);
                                                 x log(exp)
                              3 log(exp) - 1   %e
(%o5) [y(x) = x z + 2, z(x) = -------------- + ------------ + 3 x z - 2 x y]
                                 log(exp)        log(exp)
(%i6)   eqn_1: 'diff(y,x,2) - diff(y,x)= x;
                                     2
                                    d y
(%o6)                               --- = x
                                      2
                                    dx
(%i7)  eqn_2:ode2(eqn_1, y,x);
                                  3
                                 x
(%o7)                        y = -- + %k2 x + %k1
                                 6
(%i8)  eqn_3:ic2(eqn_2,x=0,y=0, 'diff(y,x)=1);
                                       3
                                      x
(%o8)                             y = -- + x
                                      6
(%i9)   plot2d(rhs(eqn_3), [x,0,3]);
plot  plot2d(rhs(eqn_3), [x,0,3]);   eqn_11: 'diff(y,x,2)- 3*diff(y,x) +4*y=x^2;
                                 2
                                d y          2
(%o10)                          --- + 4 y = x
                                  2
                                dx
(%i11)  sol: ode2(eqn_11,y,x);
                                                       2
                                                    2 x  - 1
(%o11)            y = %k1 sin(2 x) + %k2 cos(2 x) + --------
                                                       8
(%i12)  sol1: bc2(sol, x=1, y=1, x=5, y=-1);
            (7 cos(10) + 57 cos(2)) sin(2 x)
(%o12) y = -----------------------------------
           8 sin(2) cos(10) - 8 cos(2) sin(10)
                                                                          2
                                  (7 sin(10) + 57 sin(2)) cos(2 x)     2 x  - 1
                               - ----------------------------------- + --------
                                 8 sin(2) cos(10) - 8 cos(2) sin(10)      8
(%i13)  plot2d(rhs(sol1),[x,1,5]);
plot plot2d(rhs(sol1),[x,1,5]);
[assume,bc2,diff,ev] [atvalue,bc2,desolve,diff,exp,ic2,ode2,plot2d,rhs,sin] [atvalue,bc2,desolve,diff,exp,ic2,ode2,plot2d,rhs] [atvalue,bc2,desolve,diff,ic2,ode2,plot2d,rhs] [atvalue,bc2,desolve,diff,ode2,ratsimp] [atvalue,bc2,diff,ode2,plot2d,rhs] [atvalue,bc2,diff,ode2] [bc2,cos,diff,euler,integrate,ode2,plot2d,rhs,solve,subst] [bc2,cos,diff,exp,length,makelist,ode2,plot2d,rhs,rk,sin,solve,subst] [bc2,cos,diff,exp,makelist,ode2,plot2d,rhs,subst] [bc2,cos,diff,integrate,ode2,plot2d,rhs,solve,subst] [bc2,cos,diff,length,makelist,ode2,plot2d,rhs,subst] [bc2,cos,diff,numer,ode2,plot2d,rhs,sin,solve,subst] [bc2,cos,diff,numer,ode2,plot2d,rhs,solve,subst] [bc2,cos,diff,numer,ode2,plot2d,rhs,subst] [bc2,cos,diff,ode2,plot2d,rhs,subst] [bc2,cos,diff,ode2,plot2d,rhs] [bc2,cos,diff,ode2] [bc2,dependencies,depends,diff,kill,ode2] [bc2,dependencies,depends,diff,kill] [bc2,depends,diff,disp,kill,ode2] [bc2,depends,diff,integrate,kill,ode2,rhs,solve,subst] [bc2,depends,diff,kill,ode2] [bc2,depends,diff,kill] [bc2,depends,diff,ode2] [bc2,diff,euler,exp,integrate,ode2,plot2d,rhs,sin,subst] [bc2,diff,exp,first,ode2,plot2d,rhs,second,solve,subst] [bc2,diff,exp,length,makelist,ode2,plot2d,rhs,rk,subst] [bc2,diff,exp,ode2,plot2d,rhs,sin,solve,subst] [bc2,diff,exp,ode2,plot2d,rhs,solve,subst] [bc2,diff,exp,ode2,plot2d,rhs] [bc2,diff,first,ode2,plot2d,rhs,second,solve,subst] [bc2,diff,ic1,ic2,ode2,ratsimp] [bc2,diff,ic1,kill,ode2] [bc2,diff,ic2,ode2,ratsimp,sin] [bc2,diff,ic2,ode2,ratsimp] [bc2,diff,ic2,ode2] [bc2,diff,integrate,ode2,plot2d,rhs,sin] [bc2,diff,kill,ode2,plot2d,rhs,subst] [bc2,diff,numer,ode2,plot2d,rhs,solve,subst] [bc2,diff,ode2,plot2d,rhs,sin,solve,subst] [bc2,diff,ode2,plot2d,rhs,sin,subst] [bc2,diff,ode2,plot2d,rhs,solve,subst] [bc2,diff,ode2,plot2d,rhs,subst] [bc2,diff,ode2,plot2d,rhs] [bc2,diff,ode2] [bc2,diff] [bc2,ode2] [bc2]

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