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bc2-depends-diff-kill

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-dependencies-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-ic2-ode2-ratsimp

eqn3:y*('diff(y,x))^3...

soln3:ode2(eqn3,y,x);

ratsimp(ic2(soln3,x=0...

Calculate

bc2-diff-exp-ode2-plot2d-rhs
plot2d(rhs(expr), [x,-1,1]);

F:(dy)^2+4*y^2+8*y*ex...

Fy: diff(F,y);

Fdy:diff(F,dy);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-ode2-plot2d-rhs
plot2d(rhs (ps),[x,0,1],[y,-10,10]);

restart;

ecdif : 'diff(u,x,2)+...

sol2 : ode2(ecdif,u,x);

Calculate

bc2-diff-ic2-ode2-ratsimp-sin

a:x^2*'diff(y,x) + 3*...

b:ode2(a,y,x);

c:'diff(y,x,2) + y*'d...

Calculate

bc2-diff-exp-ode2-plot2d-rhs-solve-subst
plot2d([rhs(expr), rhs(expr1)],[x,-1,1]);

F:(dy)^2+4*y^2+8*y*ex...

Fy: diff(F,y);

Fdy:diff(F,dy);

Calculate

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-diff-ode2

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

sol:ode2(eqn,y,x);

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

Calculate

bc2

Run Example
(%i1)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
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;
                                                dy 2
(%o3)                      f(x, y) := 12 x y + (--)
                                                dx
(%i4) I1:diff(f(x,y),y);
(%o4)                                12 x
(%i5) I2:diff(f(x,y),'diff(y,x));
                                       dy
(%o5)                                2 --
                                       dx
(%i6) I3:diff(I2,x);
                                        2
                                       d y
(%o6)                                2 ---
                                         2
                                       dx
(%i7) y1:ode2(I1-I3=0,y,x);
                                  3
(%o7)                        y = x  + %k2 x + %k1
(%i8) h:bc2(%,x=0,y=3,x=1,y=6);
(%o8)                                 []
(%i9) 
Run Example
eqn:diff(y(x),x,2)+y=0;
                                   2
                                  d
(%o1)                         y + --- (y(x)) = 0
                                    2
                                  dx
(%i2) sol:ode2(eqn,y,x);
                                   2
                                  d
(%t2)                         y + --- (y(x)) = 0
                                    2
                                  dx

                                     msg1

(%o2)                                false
(%i3) bc2(sol, x=-1, y=1, x=1, y=-2);
(%o3)                                 []
(%i4) 

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