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diff

diff(35*q^4 -84*q^5+7...

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diff

f(x,y):=((x-y)^2+1/(1...

xx:diff(diff(f(x,y),x...

xy:diff(diff(f(x,y),x...

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diff

'diff(y,x,1)=-(%e^y-5...

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diff

f:a*t-b/t;

diff(f,t);

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diff

f=(x*x+x-3*y*y+y)/(z*...

diff(f(x));

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diff-expand-float-map-realroots

T:expand((x+5)*(x+1)*...

f(x):=''T;

NS:realroots(f(x)),fl...

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diff-ic1-ode2

eq: 'diff(ncirculi,t)...

eq2: ode2(eq,ncirculi...

sol: ic1(eq2, t = 0, ...

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diff

ec: 'diff(x^2,x,1);

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diff-ode2

eq1:'diff(y,x)=-(2*x-...

ode2(eq1,y,x);

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diff-part-solve-subst

part(part(solve(t=sub...

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diff

Run Example
(%i1)eq:'diff(y,x,2)+9*y = 9/((cos (3*x))^2);
                              2
                             d y             9
(%o1)                        --- + 9 y = ---------
                               2            2
                             dx          cos (3 x)
(%i2) ode2(eq, y, x);
          sin(3 x) log(sin(3 x) + 1) - sin(3 x) log(sin(3 x) - 1) - 2
(%o2) y = -----------------------------------------------------------
                                       2
                                                  + %k1 sin(3 x) + %k2 cos(3 x)
(%i3) 
Run Example
kill(all);
(%o0)                                done
(%i1) Ik:16;
(%o1)                                 16
(%i2) U0:92;
(%o2)                                 92
(%i3) a:I/Ik=1-(U/U0)^2;
                                            2
                                 I         U
(%o3)                            -- = 1 - ----
                                 16       8464
(%i4) l:solve(a,U);
(%o4)            [U = - 23 sqrt(16 - I), U = 23 sqrt(16 - I)]
(%i5) m:solve(a,I);
                                       2
                                      U  - 8464
(%o5)                          [I = - ---------]
                                         529
(%i6) define(I(U),rhs(m[1]));
                                         2
                                        U  - 8464
(%o6)                         I(U) := - ---------
                                           529
(%i7) define(U(I),rhs(l[2]));
(%o7)                       U(I) := 23 sqrt(16 - I)
(%i8) P(I,U):=I*U;
(%o8)                           P(I, U) := I U
(%i9) plot2d(I(U),[U,0,92], [xlabel, "U[V]"], [ylabel, "I[A]"]);
plotplot2d(I(U),[U,0,92], [xlabel, "U[V]"], [ylabel, "I[A]"]);plot2d(U(I),[I,0,16], [ylabel, "U[V]"], [xlabel, "I[A]"]);
plotplot2d(U(I),[I,0,16], [ylabel, "U[V]"], [xlabel, "I[A]"]);plot2d([P(I(U),U)],[U,0,92], [xlabel, "U[V]"], [ylabel, "P[W]"]);
plotplot2d([P(I(U),U)],[U,0,92], [xlabel, "U[V]"], [ylabel, "P[W]"]);plot2d([P(I,U(I))],[I,0,16], [xlabel, "I[A]"], [ylabel, "P[W]"], [grid, 10, 10]);
plotplot2d([P(I,U(I))],[I,0,16], [xlabel, "I[A]"], [ylabel, "P[W]"], [grid, 10, 10]);define(Iabgeleitet(U),diff(P(I(U),U),U));
                                            2    2
                                         2 U    U  - 8464
(%o13)               Iabgeleitet(U) := - ---- - ---------
                                         529       529
(%i14) define(Uabgeleitet(I),diff(P(U(I),I),I));
                                                       23 I
(%o14)        Uabgeleitet(I) := 23 sqrt(16 - I) - --------------
                                                  2 sqrt(16 - I)
(%i15) Umax:solve(Iabgeleitet(U),U);
                                  92           92
(%o15)                   [U = - -------, U = -------]
                                sqrt(3)      sqrt(3)
(%i16) Imax:solve(Uabgeleitet(I),I);
                                        32
(%o16)                             [I = --]
                                        3
(%i17) P[max]=float(Imax[1]*Umax[2]);
(%o17)                 P    = (I U = 566.5730641647529)
                        max
(%i18) R[L]=float(Umax[2]/Imax[1]);
                               U
(%o18)                   R  = (- = 4.979646071760522)
                          L    I
(%i19) 
Run Example
f:z/(1-z);
                                       z
(%o1)                                -----
                                     1 - z
(%i2) g:diff(f,z);
                                  z         1
(%o2)                          -------- + -----
                                      2   1 - z
                               (1 - z)
(%i3) expand(g);
                                  z           1
(%o3)                        ------------ + -----
                              2             1 - z
                             z  - 2 z + 1
(%i4) 
[abs,define,diff,expand,find_root,float,plot2d,realroots] [abs,define,diff,expand,find_root,float,realroots] [abs,define,diff,find_root,float,pi,plot2d] [abs,define,diff,find_root,float,realroots] [abs,define,diff,float,pi] [abs,define,diff] [abs,diff] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [assume,constant,cos,declare,diff,let,letsimp,sin,solve,trigsimp] [assume,diff,ev,integrate,plot2d,sin] [assume,diff,ev,integrate,plot2d] [assume,diff,factor,integrate,log,ratsimp] [assume,diff,integrate,plot2d] [assume,diff,ode2] [atan,diff,plot2d,solve] [atan,diff,solve] [atan,diff] [atvalue,desolve,diff] [atvalue,diff,laplace,solve] [bc2,depends,diff,kill,ode2] [cos,define,diff,expand,find_root,float,log,plot2d] [cos,define,diff,expand,float,log,plot2d] [cos,define,diff,expand,float,log] [cos,define,diff,find_root,float,plot2d,sqrt] [cos,define,diff,find_root,float,sqrt] [cos,define,diff,float,log] [cos,define,diff,float,sqrt] [cos,define,diff,sin] [cos,diff,draw,draw2d,explicit,load] [cos,diff,exp,sin] [cos,diff,exp] [cos,diff,factor,integrate,sin] [cos,diff,float,ic2,ode2,plot2d,rhs,sqrt] [cos,diff,integrate,sin] [cos,diff,log] [cos,diff,ode2] [cos,diff,plot2d,sin,sqrt] [cos,diff,plot2d,sqrt] [cos,diff,ratsimp,sin] [cos,diff,sin,solve,sqrt] [cos,diff,sin,solve] [cos,diff,sin,sqrt] [cos,diff,sin] [cos,diff,tan] [cos,diff] [define,diff,expand,float,plot2d,sin] [define,diff,expand,float,sin] [define,diff,expand] [define,diff,find_root,float,log,sin] [define,diff,find_root,log,sin]

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