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### Related

##### bc2-cos-diff-ode2-plot2d-rhs

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

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

x1:0;

x2:2;

Calculate

##### bc2-cos-diff-ode2-plot2d-rhs

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

Fy:diff(F,y);

Fdy:diff(F,Dy);

Calculate

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

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

x1:0;

x2:2;

Calculate

##### bc2-cos-diff-ode2-plot2d-rhs

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

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

x1:0;

x2:2;

Calculate

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

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

x1:0;

x2:2;

Calculate

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

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

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

x1:0;

x2:2;

Calculate

##### bc2-cos-diff-ode2-plot2d-rhs

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)"]);
plot```
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]);
plot```
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]);
plot```

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