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bc2-diff-ic2-ode2-ratsimp

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

soln3:ode2(eqn3,y,x);

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

Calculate

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

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

Fy:diff(F,y);

Fdy:diff(F,Dy);

Calculate

bc2-diff-ode2

ode2('diff(y,x,2)-10*...

bc2(%,x=0,y=1,x=1,y=0);

Calculate

bc2-depends-diff-kill

kill(all);

dpends(f[x,y]);

depends(y,x);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-ic2-ode2-tan

eq: 'diff(y, t, 2) + ...

ode2(eq, y, t);

sol2: ode2(eq, y, t);

Calculate

bc2-diff-integrate-ode2-plot2d-rhs-sin
plot2d(rhs (ps),[x,0,1],[y,0,0.10]);

restart;

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

sol2 : ode2(ecdif,u,x);

Calculate

bc2-dependencies-depends-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-cos-diff

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

bc2(%o1,x=0,y=1.06883...

Calculate

bc2-diff-ic2-ode2-ratsimp

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

soln3:ode2(eqn3,y,x);

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

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
kill(all);
(%o0)                                done
(%i1) depends(f,[x,y]);
(%o1)                              [f(x, y)]
(%i2) depends(y,x);
(%o2)                               [y(x)]
(%i3) dependencies;
(%o3)                           [f(x, y), y(x)]
(%i4) f(x,y):=(1+('diff(y,x)))^(1/2);
                                            dy 1/2
(%o4)                       f(x, y) := (1 + --)
                                            dx
(%i5) l2:diff(y,x,2)=0;
                                     2
                                    d y
(%o5)                               --- = 0
                                      2
                                    dx
(%i6) Y1:ode2(l12,y,x);
(%t6)                                 l12

                                     msg1

(%o6)                                false
(%i7) bc2(%,x=0,y=1,x=1,y=2);
(%o7)                                 []
(%i8) 

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