### Related

##### bc2-diff-ode2

eq:'diff(y,x) = 15-y^3;

ode2(eq, y, x);

bc2(%o2,x=0,y=1,x=1,y...

Calculate

##### bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

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-length-makelist-ode2-plot2d-rhs-rk-sin-solve-subst

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

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

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

restart;

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

sol2 : ode2(ecdif,u,x);

Calculate

##### bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

##### bc2-cos-diff-numer-ode2-plot2d-rhs-solve-subst

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

x1:-1;

x2:1;

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-ode2

eq: 'diff(y,x,2)-y=%e...

so: ode2(eq,y,x);

bc2(so, x=1, y=1, x=5...

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   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```

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