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logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(x-5);

f1:logcontract(f);

Calculate

logcontract

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(x-5);

f:logcontract(f);

Calculate

logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1)+log2(X-5);

g:logcontract(f);

Calculate

logcontract-rat-ratsimpexpons-ratsubst-true

a:(x^k-1)/(2^k-1);

b:(x^k-x-1)/(2^k-2);

c: rat(b-a);

Calculate

logcontract

f:log2(x+1)+log2(x-5)=4;

g:logcontract(f);

Calculate

logcontract

logcontract(log(x)+lo...

Calculate

logcontract

log2(x):=log(2)/log(x);

f:log2(x+1)+log2(x-5);

g:logcontract(f);

Calculate

logcontract-solve

log2(x):=log(x)/log(2);

f:log2(x+1);

log2(x-5);

Calculate

logcontract

logcontract(log(a)+lo...

Calculate

logcontract-rat-ratsimpexpons-ratsubst-true

a:(x^k-1)/(2^k-1);

b:(x^k-x-1)/(2^k-2);

c: rat(b-a);

Calculate

logcontract

Run Example
(%i1)e1: 2*(2*a*log(y)+a*log(x));
(%o1)                      2 (2 a log(y) + a log(x))
(%i2) logcontract(e1);
                                        2  4
(%o2)                            a log(x  y )
(%i3) e2:-4*log(4)/3  + log(3)+ 2 *log(2) + 1;
                        4 log(4)
(%o3)                 - -------- + log(3) + 2 log(2) + 1
                           3
(%i4)  logcontract(e2);
                                      4 log(4)
(%o4)                       log(12) - -------- + 1
                                         3
(%i5) 
Run Example
eq1 : 'diff(P,t) = P*(a-b*P);
                               dP
(%o1)                          -- = P (a - b P)
                               dt
(%i2) gsoln : ode2(eq1, P,t), logcontract;
                                    P
                             log(-------)
                                 b P - a
(%o2)                        ------------ = t + %c
                                  a
(%i3) gsoln : gsoln * denom(lhs(gsoln));
                                  P
(%o3)                      log(-------) = a (t + %c)
                               b P - a
(%i4) gsoln : exp(lhs(gsoln)) = exp(rhs(gsoln));
                               P        a (t + %c)
(%o4)                       ------- = %e
                            b P - a
(%i5) psoln : ic1(gsoln, t=0, P=3929);
                                              a t
                                P      3929 %e
(%o5)                        ------- = ----------
                             b P - a   3929 b - a
(%i6) ps1 : ev(psoln, t=6, P=23192);
                                                6 a
                              23192      3929 %e
(%o6)                      ----------- = ----------
                           23192 b - a   3929 b - a
(%i7) ps2 : ev(psoln, t=12, P=91972);
                                                12 a
                              91972      3929 %e
(%o7)                      ----------- = -----------
                           91972 b - a   3929 b - a
(%i8) ps2 : solve(ps2, b);
                                      12 a
                             3929 a %e     - 91972 a
(%o8)                 [b = ----------------------------]
                                       12 a
                           361357988 %e     - 361357988
(%i9) 
Run Example
/* SETUP DE */de : 'diff(x,t) = sin(x);
                                  dx
(%o1)                             -- = sin(x)
                                  dt
(%i2) sol : ode2(de,x,t);
                   log(cos(x) + 1) - log(cos(x) - 1)
(%o2)            - --------------------------------- = t + %c
                                   2
(%i3) sol : logcontract(2*sol);
                             cos(x) - 1
(%o3)                    log(----------) = 2 t + 2 %c
                             cos(x) + 1
(%i4) sol : map(exp,sol);
                           cos(x) - 1     2 t + 2 %c
(%o4)                      ---------- = %e
                           cos(x) + 1
(%i5) sol : ratsubst(%A,exp(2*%c),sol);
                             cos(x) - 1        2 t
(%o5)                        ---------- = %A %e
                             cos(x) + 1
(%i6) cosx : first(solve(sol,cos(x)));
                                            2 t
                                       %A %e    + 1
(%o6)                       cos(x) = - ------------
                                            2 t
                                       %A %e    - 1
(%i7) s : first(solve(cosx,x));

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                        2 t
                                   %A %e             1
(%o7)             x = %pi - acos(------------ + ------------)
                                      2 t            2 t
                                 %A %e    - 1   %A %e    - 1
(%i8) s : ratsimp(s);
                                             2 t
                                        %A %e    + 1
(%o8)                    x = %pi - acos(------------)
                                             2 t
                                        %A %e    - 1
(%i9) load(draw);
(%o9)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i10) draw2d(explicit(subst(%A=1,s),t,-5,5),grid=true);
plotdraw2d(explicit(subst(%A=1,s),t,-5,5),grid=true);

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