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bc2-diff-ic1-ic2-ode2-ratsimp

egn1:'diff(y,x)+y=0;

soln1:ode2(egn1,y,x);

ic1(soln1,x=0,y=3);

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"]);

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

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

x1:-1;

Calculate

bc2-diff-ode2

v:v_t(r);

'diff((1/r)*'diff(r*v...

diffeq:diff((1/r)*dif...

Calculate

bc2-ode2

diffeq:'diff((1/r)*'d...

ode2:(diffeq,v,r);

bc2(%o4,r=k*R,v=R*O_i...

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
 plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

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

x1:0;

x2:2;

Calculate

bc2-depends-diff-kill

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-ic1-ode2

eq:'diff(y,x) = -xy ...

sol: ode2(eq,y,x);

ic1(sol, x= 0, y= 0);

Calculate

bc2-dependencies-depends-diff-kill-ode2

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-ode2-plot2d-rhs
plot2d(rhs(c11), [x, -1, 1]);

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

sol: ode2(eqn,y,x);

c11: bc2(sol, x=-1, y...

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
eqn:diff(y,x,2)+y=0;
(%o1)                                y = 0
(%i2)           sol:ode2(eqn,y,x);
(%t2)                                y = 0

                                     msg1

(%o2)                                false
(%i3)           eqnend:bc2(sol, x=-1, y=1, x=1, y=-2);
(%o3)                                 []
(%i4)           plot2d(rhs(eqnend),[x,-1,2],[xlabel,"x"],[ylabel,"y(x)"]);
plot          plot2d(rhs(eqnend),[x,-1,2],[xlabel,"x"],[ylabel,"y(x)"]);

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