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assume-diff-ev-facts-integrate-rhs

(assume (x*y>0),fa...

integrate(%e^(-t^2),t...

f(x,y)=integrate(%e^(...

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assume(l>0);

assume(E>0);

assume(S>0);

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assume-integrate

f(x):= 1/x^(1/2);

assume (L>0);

integrate(f(x)^2,x,-L...

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assume-atvalue-diff-laplace-limit-solve

assume(R0>0, R1>...

atvalue(vc(t),t=0,Vc0);

atvalue(il(t),t=0,Il0);

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assume (t>0);

assume (T>0);

erfflag:false;

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assume-constant-cos-declare-diff-expandwrt_factored-globalsolve-let-letsimp-posfun-ratcoef-realonly-sin-subst-tlimswitch-trigsimp-true

globalsolve: true;

realonly: true;

/* Standard (x,y)->...

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assume-cos-integrate-sin

assume(a>0);

assume (b>0);

integrate(1/((a*(cos...

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assume-diff-integrate-plot2d

/* [wxMaxima batch fi...

dy(x):=diff(y(x),x);

ddy(x):=diff(dy(x),x);

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assume (t>0);

assume (T>0);

erfflag:false;

Calculate

assume-exp-inf-integrate-log

assume(a>0);

fm(v):=4*%pi*n/%pi^(3...

lfm(v):=(-v^2/a^2)+lo...

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assume

Run Example
```(%i1)assume(V>
0, R>
0, L>
0, C>
0);
(%o1)                    [V > 0, R > 0, L > 0, C > 0]
(%i2) assume(C*R^2 - 4*L >
0);
2
(%o2)                            [C R  > 4 L]
(%i3) ec  : R*x(t) + L*diff(x(t),t) + integrate(x(t), t)/C = V;
/
[
I x(t) dt
]
d              /
(%o3)               x(t) R + (-- (x(t))) L + --------- = V
dt                 C
(%i4) ecd : diff(ec, t);
2
d               d               x(t)
(%o4)              (-- (x(t))) R + (--- (x(t))) L + ---- = 0
dt                2              C
dt
(%i5) e2:laplace(ecd,t,s);
!
d        !
(%o5) (s laplace(x(t), t, s) - x(0)) R + (- -- (x(t))!
dt       !
!t = 0
2                                   laplace(x(t), t, s)
+ s  laplace(x(t), t, s) - x(0) s) L + ------------------- = 0
C
(%i6) atvalue( x(t), t=0, 0);
(%o6)                                  0
(%i7) atvalue( diff(x(t), t), t=0, V/L);
V
(%o7)                                  -
L
(%i8) e4:solve(e2,laplace(x(t),t,s));
!
d        !
x(0) C R + (-- (x(t))!      + x(0) s) C L
dt       !
!t = 0
(%o8)  [laplace(x(t), t, s) = -----------------------------------------]
2
s C R + s  C L + 1
(%i9) ilt(e2,s,t);
(%o9) ilt((s laplace(x(t), t, s) - x(0)) R, s, t)
!
d        !         2
+ ilt((- -- (x(t))!      + s  laplace(x(t), t, s) - x(0) s) L, s, t)
dt       !
!t = 0
laplace(x(t), t, s)
+ ilt(-------------------, s, t) = 0
C
(%i10) ```
Run Example
```assume(A>
0,d>
0,y>
0,%lambda>
0,D>
0);
(%o1)              [A > 0, d > 0, y > 0, %lambda > 0, D > 0]
(%i2) test:4*A^2*cos(%pi*d*y/(%lambda*D))^2;
2    2  %pi d y
(%o2)                        4 A  cos (---------)
%lambda D
(%i3) l:diff(test,y,1);
2      %pi d y        %pi d y
8 %pi d A  cos(---------) sin(---------)
%lambda D      %lambda D
(%o3)             - ----------------------------------------
%lambda D
(%i4) solve(l=0,y);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
%lambda D
(%o4)                       [y = 0, y = ---------]
2 d
(%i5) ```
Run Example
```assume(r>
0);
(%o1)                               [r > 0]
(%i2) assume(d>
0);
(%o2)                               [d > 0]
(%i3) assume(b>
0);
(%o3)                               [b > 0]
(%i4) rr(t):=sqrt(r*r+rp*rp-2*r*rp*cos(t));
(%o4)           rr(t) := sqrt(r r + rp rp + (- 2) r rp cos(t))
(%i5) x(t):=rr(t)/(2*d);
rr(t)
(%o5)                            x(t) := -----
2 d
(%i6) f(t):=1/d*(6/5-2*x(t)^2+3/2*x(t)^3-5*x(t)^5);
1  6      2      3  3             5
(%o6)           f(t) := - (- - 2 x (t) + - x (t) + (- 5) x (t))
d  5             2
(%i7) expand(f(t)*sin(t));
2    2 5/2
5 (- 2 r rp cos(t) + rp  + r )    sin(t)
(%o7) - ----------------------------------------
6
32 d
2    2 3/2                                 2
3 (- 2 r rp cos(t) + rp  + r )    sin(t)   r rp cos(t) sin(t)   rp  sin(t)
+ ---------------------------------------- + ------------------ - ----------
4                              3                 3
16 d                              d               2 d
2
r  sin(t)   6 sin(t)
- --------- + --------
3        5 d
2 d
(%i8) integrate(expand(f(t)*sin(t)),t);
2    2 7/2                          2    2 5/2
5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o8) - --------------------------------- + ---------------------------------
6                                  4
224 d  r rp                         80 d  r rp
2        2           2
r rp cos (t)   rp  cos(t)   r  cos(t)   6 cos(t)
- ------------ + ---------- + --------- - --------
3             3           3        5 d
2 d           2 d         2 d
(%i9) integrate(f(t)*sin(t),t);
2    2 7/2                          2    2 5/2
5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o9) (- --------------------------------- + ---------------------------------
5                                  3
224 d  r rp                         80 d  r rp
2        2           2
- r rp cos (t) + rp  cos(t) + r  cos(t)   6 cos(t)
+ --------------------------------------- - --------)/d
2                        5
2 d
(%i10) ```

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