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ic1

ic1(P=%c*%e^(r*t),P=P...

Calculate

ic1

ic1(P=%c*%e^(r*t),P=P...

Calculate

ic1

Run Example
(%i1)eq: 'diff(l,t) = k * (a - l);
                                dl
(%o1)                           -- = k (a - l)
                                dt
(%i2) eq2: ode2(eq,l,t);
                                - k t      k t
(%o2)                     l = %e      (a %e    + %c)
(%i3) sol: ic1(eq2, t= b, l= 0);
                              - k t      k t       b k
(%o3)                   l = %e      (a %e    - a %e   )
(%i4) 
Run Example
eq:'diff(y,x)-x*y=x;
                                 dy
(%o1)                            -- - x y = x
                                 dx
(%i2) sol1:ode2(eq,y,x);
                                           2     2
                                          x     x
                                        - --    --
                                          2     2
(%o2)                       y = (%c - %e    ) %e
(%i3) sol2:ic1(sol1,y=0,x=2);
                                          2
                                         x
                                         --
                                  - 2    2      2
(%o3)                       y = %e    (%e   - %e )
(%i4) 
Run Example
eq: 'diff(y,x)=-.5 * (100 -x);
                             dy
(%o1)                        -- = - 0.5 (100 - x)
                             dx
(%i2) eq1: ode2(eq,y,x);

rat: replaced 50.0 by 50/1 = 50.0

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced 50.0 by 50/1 = 50.0

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced 50.0 by 50/1 = 50.0

rat: replaced -0.5 by -1/2 = -0.5
                                   2
                                  x
                                  -- - 100 x
                                  2
(%o2)                         y = ---------- + %c
                                      2
(%i3) sol: ic1(eq1, x=0, y=1000);
                                  2
                                 x  - 200 x + 4000
(%o3)                        y = -----------------
                                         4
(%i4) 
[assume,diff,ev,false,float,fpprintprec,ic1,inf,kill,lambda,limit,map,numer,ode2,ratprint,ratsimp,rhs,solve,subst] [assume,diff,ev,ic1,ic2,ode2,plot2d] [assume,diff,ic1,ic2,ode2] [assume,diff,ic1,ode2] [cos,diff,ic1,ode2,plot2d,rhs] [define,denom,diff,ev,exp,ic1,lhs,load,logcontract,ode2,plot2d,ratsimp,rhs,solve] [define,depends,diff,ev,ic1,ode2,rhs] [denom,diff,ev,exp,ic1,lhs,load,logcontract,ode2,ratsimp,rhs,solve] [denom,diff,ev,exp,ic1,lhs,logcontract,ode2,rhs,solve] [diff,disp,ic1,ode2,print,rhs,tan] [diff,disp,ic1,ode2,print,rhs] [diff,display,ic1,ode2,solve] [diff,do,expand,ic1,ode2] [diff,do,ic1,ode2,plot2d,rhs] [diff,do,ic1,ode2,ratsimp,subst] [diff,do,ic1,ode2,subst] [diff,do,ic1,ode2] [diff,ev,exp,ic1,ode2,solve] [diff,ev,float,ic1,ode2] [diff,ev,fpprintprec,ic1,numer,ode2,true] [diff,exp,false,ic1,ode2,plot2d,ratprint,ratsimp,rhs,subst] [diff,exp,false,ic1,ode2,plot2d,ratprint,ratsimp,rhs] [diff,exp,ic1,log,ode2,plot2d] [diff,exp,ic1,log,ode2,solve] [diff,exp,ic1,ode2,solve] [diff,exp,ic1,ode2] [diff,factor,ic1,ode2] [diff,false,ic1,kill,load,logabs,ratprint,reset,true] [diff,false,ic1,ode2,plot2d,ratprint,ratsimp,rhs] [diff,false,ic1,ode2,plot2d,ratprint,remvalue,rhs] [diff,fullratsimp,ic1,ode2] [diff,ic1,ic2,ode2] [diff,ic1,integrate,ode2] [diff,ic1,kill,ode2,plot2d,rhs] [diff,ic1,kill,ode2,plot2d] [diff,ic1,kill,ode2] [diff,ic1,linsolve,ode2] [diff,ic1,log,ode2,plot2d] [diff,ic1,ode2,plot2d,rhs,sin] [diff,ic1,ode2,plot2d,rhs] [diff,ic1,ode2,plot2d] [diff,ic1,ode2,ratsimp] [diff,ic1,ode2,ratsubst] [diff,ic1,ode2,rhs,sin] [diff,ic1,ode2,sin] [diff,ic1,ode2,solve,sqrt] [diff,ic1,ode2,solve] [diff,ic1,ode2,sqrt] [diff,ic1,ode2,subst] [diff,ic1,ode2]

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