## How can I solve this ODE with an integral by dsolv...

ode := D(c)(t) = (ln(c(t)) + w - p*c(t))*(c(t)(t + 1/int(c(h), h = 0 .. t)) + int(c(h), h = 0 .. t))/(p - 1/c(t))

I have such differential equation derived from Euler-Lagrange condition of calculus of variation problem.

I tried to solve it, but it says there are two c(t) and c(h). c(t) is what I want to get.

Thank you

## how to achieve this animation ?...

; restart; with(plots); _local(O); P := b*x*cos(phi)+a*y*sin(phi)-a . b = 0; P := b x cos(phi) + a y sin(phi) - a . b = 0 Q := a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi) = 0; 2 Q := a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) = 0 M := op(solve([P, Q], [x, y])); M := [subs(M, x), subs(M, y)]; X := &-+(P/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2)); Y := &-+(Q/sqrt(b^2*cos(phi)^2+a^2*sin(phi)^2)); #L'équation générale des coniques ayant pour axes MN et MT est, par rapport aux nouveaux axes de coordonnées X^2/A+Y^2/B-1 = (0*et)*par*rapport*aux*anciens; P^2/(A*(b^2*cos(phi)^2+a^2*sin(phi)^2))+Q^2/(B*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0; 2 /b x cos(phi) + a y sin(phi) - a . b \ &-+|----------------------------------- = 0| | (1/2) | |/ 2 2 2 2\ | \\a sin(phi) + cos(phi) b / / --------------------------------------------- A 2 / 2 \ |a x sin(phi) - b y cos(phi) - c sin(phi) cos(phi) | &-+|-------------------------------------------------- = 0| | (1/2) | | / 2 2 2 2\ | \ \a sin(phi) + cos(phi) b / / + ------------------------------------------------------------ B - 1 = 0 #1.-Ecrivons que la conique (1) est tangente en O à Oy : il faut pour cela annuler le coefficient de y et le terme indépendant. #Nous obtenons 2 équations en A et B, d'où nous tirons : A=a² et B=c²cos(phi)² a := 10; b := 7; c := sqrt(a^2-b^2); phi := 4*Pi*(1/5); Ell := implicitplot(x^2/a^2+y^2/b^2-1 = 0, x = -11 .. 11, y = -8 .. 8, color = grey); O := [0, 0]; M := [a*cos(phi), b*sin(phi)]; vec := plot([O, M], color = black, thickness = 1); P := implicitplot(P, x = -20 .. 20, y = -20 .. 20, color = aquamarine); Q := implicitplot(Q, x = -20 .. 20, y = -20 .. 20); F1 := [(a+b)*cos(phi), (a+b)*sin(phi)]; F2 := [2*M[1]-F1[1], 2*M[2]-F1[2]]; F1F2 := plot([F1, F2], color = green, thickness = 3); ELL := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(a^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(c^2*cos(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = blue, thickness = 3); Hyp := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)^2/(b^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))^2/(-c^2*sin(phi)^2*(b^2*cos(phi)^2+a^2*sin(phi)^2))-1 = 0, x = -20 .. 20, y = -20 .. 20, color = black); dF1 := plottools[disk](F1, .3, color = red); dF2 := plottools[disk](F2, .3, color = red); cir1 := implicitplot(x^2+y^2 = (a+b)^2, x = -20 .. 20, y = -18 .. 18, color = pink); cir2 := implicitplot(x^2+y^2 = (a-b)^2, x = -10 .. 10, y = -4 .. 4, color = coral); asym1 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b+(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT); asym2 := implicitplot((b*x*cos(phi)+a*y*sin(phi)-a . b)/b-(a*x*sin(phi)-b*y*cos(phi)-c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT); tp := textplot([[M[1], M[2]+.8, "M"], [F1[1]-.8, F1[2], "F1"], [F2[1]+.8, F2[2]+.3, "F2"], [5, 15, "axe P"], [8, -10, "axe Q"]]); display([Ell, vec, P, Q, F1F2, cir1, cir2, ELL, Hyp, dF1, dF2, asym1, asym2, tp], scaling = constrained, axes = normal, axis = [gridlines = [1, color = blue]], xtickmarks = 0, ytickmarks = 0, view = [-20 .. 20, -20 .. 20], size = [500, 500]); #Eléments fixes : Ell, cir1, cir2, O #Parties mobiles : ELL, Hyp, P,Q, M,F1, F2, # FIGURE MOBILE n := 100; dt := 2*Pi/n; Phi := 0; P := b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b = 0; Q := a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt) = 0; M := [cos(phi+dt)*(sin(phi+dt)^2*a*c^2+Typesetting[delayDotProduct](a . b, b, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2), sin(phi+dt)*(-cos(phi+dt)^2*b*c^2+Typesetting[delayDotProduct](a . b, a, true))/(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2)]; ELL := (b*x*cos(phi+dt)+a*y*sin(phi+dt)-a . b)^2/(a^2*(a^2*sin(phi+dt)^2+cos(phi+dt)^2*b^2))+(a*x*sin(phi+dt)-b*y*cos(phi+dt)-c^2*sin(phi+dt)*cos(phi+dt))^2/(c^2*cos(phi+dt)^2*(cos(phi+dt)^2*b^2+a^2))-1 = 0; NULL; display([Ell, cir1, cir2], scaling = constrained);

## Solving non linear differential equation ...

Hi,

I was attempting to solve an ODE, but it does not turn out anything. It is a bit complicated ODE. dsolve turns nothing, and I tried little different specification for an end point or initial point, but it calculates like forever giving nothing. What shall I do?

ode := 0 = diff(y(x), x) + ((r + 2*x)*(p - y(x)^(-s)))/(-(b*y(x) - x^2)*s*y(x)^(-s - 1))

parameters(0 < r, 0 < p, b < 1 and 0 < b, 0 < s)

## trigonometric function error...

hi

can anyone help me with this error.

why maple2019 gives result of trigonometric function in terms of I.

snapshot attached

## minimizing integral using minimize...

I am tryoing to optimize an integral which gives

Error, (in Optimization:-NLPSolve) invalid arguments

## How do I find the asymptote of a function?...

What is the proper sequence of commends which will yield the asymptoe of a given function of a single variable?

## How to compute the arc length parametrization for ...

I have an arc length parametrization question. The problem says to find a function g(s) that you can use to calculate the arc length parametrization, then find a formula for the arc length parametrization. I have r(t)= <cos(2t), sin(3t), 4t>. How would I do this?

## solve set satisfy problem...

restart;
P := -lambda*exp(-Phi(xi))-mu*exp(Phi(xi));
-lambda exp(-Phi(xi)) - mu exp(Phi(xi))
u[0] := A[0]+A[1]*exp(-Phi(xi))+A[2]*exp(-Phi(xi))*exp(-Phi(xi));
2
A[0] + A[1] exp(-Phi(xi)) + A[2] (exp(-Phi(xi)))
u[1] := diff(u[0], xi);
/ d          \
-A[1] |---- Phi(xi)| exp(-Phi(xi))
\ dxi        /

2 / d          \
- 2 A[2] (exp(-Phi(xi)))  |---- Phi(xi)|
\ dxi        /
d[1] := -A[1]*P*exp(-Phi(xi))-2*A[2]*(exp(-Phi(xi)))^2*P;
-A[1] (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(-Phi(xi)) - 2

2
A[2] (exp(-Phi(xi)))  (-lambda exp(-Phi(xi)) - mu exp(Phi(xi)))
u[2] := diff(d[1], xi);
/       / d          \
-A[1] |lambda |---- Phi(xi)| exp(-Phi(xi))
\       \ dxi        /

/ d          \             \
- mu |---- Phi(xi)| exp(Phi(xi))| exp(-Phi(xi)) + A[1] (
\ dxi        /             /
/ d          \
-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) |---- Phi(xi)| exp(-Phi(
\ dxi        /

2
xi)) + 4 A[2] (exp(-Phi(xi)))  (-lambda exp(-Phi(xi))

/ d          \                         2
- mu exp(Phi(xi))) |---- Phi(xi)| - 2 A[2] (exp(-Phi(xi)))
\ dxi        /

/       / d          \
|lambda |---- Phi(xi)| exp(-Phi(xi))
\       \ dxi        /

/ d          \             \
- mu |---- Phi(xi)| exp(Phi(xi))|
\ dxi        /             /

d[2] := -A[1]*(lambda*P*exp(-Phi(xi))-mu*P*exp(Phi(xi)))*exp(-Phi(xi))+A[1]*(-lambda*exp(-Phi(xi))-mu*exp(Phi(xi)))*P*exp(-Phi(xi))+4*A[2]*(exp(-Phi(xi)))^2*(-lambda*exp(-Phi(xi))-mu*exp(Phi(xi)))*P-2*A[2]*(exp(-Phi(xi)))^2*(lambda*P*exp(-Phi(xi))-mu*P*exp(Phi(xi)));
-A[1] (lambda (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(-Phi(

xi))

- mu (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(Phi(xi)))

exp(-Phi(xi))

2
+ A[1] (-lambda exp(-Phi(xi)) - mu exp(Phi(xi)))  exp(-Phi(xi)) + 4

2
A[2] (exp(-Phi(xi)))

2
(-lambda exp(-Phi(xi)) - mu exp(Phi(xi)))  - 2 A[2]

2
(exp(-Phi(xi)))  (lambda (-lambda exp(-Phi(xi))

- mu exp(Phi(xi))) exp(-Phi(xi))

- mu (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(Phi(xi)))

collect(expand((2*k*k)*w*beta*d[2]-(2*alpha*k*k)*d[1]-2*w*u[0]+k*u[0]*u[0]), exp(Phi(xi)));
2               2            2                 2
4 k  w beta A[2] mu  - 2 alpha k  A[1] mu + k A[0]  - 2 w A[0] +

1       /        2                             2
------------ \4 beta k  lambda mu w A[1] - 4 alpha k  mu A[2]
exp(Phi(xi))

\          1        /         2
+ 2 k A[0] A[1] - 2 w A[1]/ + --------------- \16 beta k
2
(exp(Phi(xi)))

2
lambda mu w A[2] - 2 alpha k  lambda A[1] + 2 k A[0] A[2]

2           \          1        /        2       2
+ k A[1]  - 2 w A[2]/ + --------------- \4 beta k  lambda  w A
3
(exp(Phi(xi)))

2                            \
[1] - 4 alpha k  lambda A[2] + 2 k A[1] A[2]/

2       2                2
12 beta k  lambda  w A[2] + k A[2]
+ -----------------------------------
4
(exp(Phi(xi)))

restart;
solve({12*beta*k^2*lambda^2*w*A[2]+k*A[2]^2, 4*beta*k^2*lambda^2*w*A[1]-4*alpha*k^2*lambda*A[2]+2*k*A[1]*A[2], 4*beta*k^2*mu^2*w*A[2]-2*alpha*k^2*mu*A[1]+k*A[0]^2-2*w*A[0], 4*beta*k^2*lambda*mu*w*A[1]-4*alpha*k^2*mu*A[2]+2*k*A[0]*A[1]-2*w*A[1], 16*beta*k^2*lambda*mu*w*A[2]-2*alpha*k^2*lambda*A[1]+2*k*A[0]*A[2]+k*A[1]^2-2*w*A[2]}, {k, w, A[0], A[1], A[2]});
{k = 0, w = 0, A[0] = A[0], A[1] = A[1], A[2] = A[2]},

{k = k, w = w, A[0] = 0, A[1] = 0, A[2] = 0},

/
/                     2 w                    \    |
{ k = k, w = w, A[0] = ---, A[1] = 0, A[2] = 0 }, <
\                      k                     /    |
\

/                    2    \
k = RootOf\24 beta lambda mu _Z  - 1/,

/                2    \
RootOf\100 lambda mu _Z  + 1/ alpha
w = -----------------------------------,
beta

/                2    \
RootOf\100 lambda mu _Z  + 1/ alpha
A[0] = ----------------------------------------,
/                    2    \
2 beta RootOf\24 beta lambda mu _Z  - 1/

alpha
A[1] = --------------------------------------------, A[2] = -12
/                    2    \
10 beta mu RootOf\24 beta lambda mu _Z  - 1/

/                    2    \       2       /
RootOf\24 beta lambda mu _Z  - 1/ lambda  RootOf\100 lambda mu

\    /
2    \      |    |          /                    2    \
_Z  + 1/ alpha >, < k = RootOf\24 beta lambda mu _Z  + 1/,
|    |
/    \

/                2    \
RootOf\100 lambda mu _Z  + 1/ alpha
w = -----------------------------------,
beta

/                2    \
3 RootOf\100 lambda mu _Z  + 1/ alpha
A[0] = ----------------------------------------,
/                    2    \
2 beta RootOf\24 beta lambda mu _Z  + 1/

alpha
A[1] = - --------------------------------------------, A[2] = -
/                    2    \
10 beta mu RootOf\24 beta lambda mu _Z  + 1/

/                    2    \       2       /
12 RootOf\24 beta lambda mu _Z  + 1/ lambda  RootOf\100 lambda

\
2    \      |
mu _Z  + 1/ alpha >
|
/
set 1;
Error, missing operation
Typesetting:-mambiguous(Typesetting:-mambiguous(set 1,

Typesetting:-merror("missing operation")))
{k = RootOf(24*_Z^2*beta*lambda*mu-1), w = RootOf(100*_Z^2*lambda*mu+1)*alpha/beta, A[0] = (1/2)*RootOf(100*_Z^2*lambda*mu+1)*alpha/(beta*RootOf(24*_Z^2*beta*lambda*mu-1)), A[1] = (1/10)*alpha/(beta*mu*RootOf(24*_Z^2*beta*lambda*mu-1)), A[2] = -12*RootOf(24*_Z^2*beta*lambda*mu-1)*lambda^2*RootOf(100*_Z^2*lambda*mu+1)*alpha};
/
|          /                    2    \
< k = RootOf\24 beta lambda mu _Z  - 1/,
|
\

/                2    \
RootOf\100 lambda mu _Z  + 1/ alpha
w = -----------------------------------,
beta

/                2    \
RootOf\100 lambda mu _Z  + 1/ alpha
A[0] = ----------------------------------------,
/                    2    \
2 beta RootOf\24 beta lambda mu _Z  - 1/

alpha
A[1] = --------------------------------------------, A[2] = -12
/                    2    \
10 beta mu RootOf\24 beta lambda mu _Z  - 1/

/                    2    \       2       /
RootOf\24 beta lambda mu _Z  - 1/ lambda  RootOf\100 lambda mu

\
2    \      |
_Z  + 1/ alpha >
|
/
restart;
restart;
solve({24*Z^2*beta*lambda*mu-1}, {Z});
/              (1/2)         \
|             6              |
< Z = ------------------------ >,
|                       (1/2)|
\    12 (beta lambda mu)     /

/                (1/2)         \
|               6              |
< Z = - ------------------------ >
|                         (1/2)|
\      12 (beta lambda mu)     /
solve({100*Z^2*lambda*mu+1}, {Z});
/               1          \    /             1          \
|Z = - --------------------| ,  |Z = --------------------|
<                      (1/2) >  <                    (1/2) >
|      10 (-lambda mu)     |    |    10 (-lambda mu)     |
\                          /    \                        /
restart;
k := (1/12)*sqrt(6)/sqrt(beta*lambda*mu);
(1/2)
6
------------------------
(1/2)
12 (beta lambda mu)
w := -alpha/((10*sqrt(-lambda*mu))*beta);
alpha
- -------------------------
(1/2)
10 (-lambda mu)      beta
A[0] := 1/2*(-alpha/((10*sqrt(-lambda*mu))*((1/12)*beta*sqrt(6)/sqrt(beta*lambda*mu))));
(1/2)                 (1/2)
alpha 6      (beta lambda mu)
- ----------------------------------
(1/2)
10 (-lambda mu)      beta
A[1] := (1/10)*alpha/((1/12)*beta*mu*sqrt(6)/sqrt(beta*lambda*mu));
(1/2)                 (1/2)
alpha 6      (beta lambda mu)
----------------------------------
5 beta mu
A[2] := (12*(1/12))*sqrt(6)*lambda^2*alpha/(sqrt(beta*lambda*mu)*(10*sqrt(-lambda*mu)));
(1/2)       2
6      lambda  alpha
------------------------------------------
(1/2)             (1/2)
10 (beta lambda mu)      (-lambda mu)
lambda := 3;
3
mu := 2;
2
H := -ln(sqrt(lambda/mu)*tan(sqrt(lambda*mu)*(xi+C)));
/1  (1/2)    / (1/2)         \\
-ln|- 6      tan\6      (xi + C)/|
\2                            /
u[0] := A[0]+A[1]*exp(-H)+A[2]*exp(-H)*exp(-H);
(1/2)            (1/2)    / (1/2)         \
alpha (-6)        3 alpha 6      tan\6      (xi + C)/
--------------- + -----------------------------------
(1/2)                       (1/2)
10 beta                     10 beta

2
(1/2)    / (1/2)         \
9 alpha (-6)      tan\6      (xi + C)/
- ---------------------------------------
(1/2)
40 beta
f := diff(u[0], xi);
/                        2\
|       / (1/2)         \ |                /
9 alpha \1 + tan\6      (xi + C)/ /        1       |
----------------------------------- - ------------ \9 alpha
(1/2)                      (1/2)
5 beta                    20 beta

/                        2\
(1/2)    / (1/2)         \ |       / (1/2)         \ |
(-6)      tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ /

\
(1/2)|
6     /
S := diff(f, xi);
/                        2\
/ (1/2)         \ |       / (1/2)         \ |  (1/2)
18 alpha tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ / 6
----------------------------------------------------------------
(1/2)
5 beta

2
/                        2\
(1/2) |       / (1/2)         \ |
27 alpha (-6)      \1 + tan\6      (xi + C)/ /
- ----------------------------------------------- -
(1/2)
10 beta

/                                       2 /
1      |             (1/2)    / (1/2)         \  |
----------- \27 alpha (-6)      tan\6      (xi + C)/  \1
(1/2)
5 beta

2\\
/ (1/2)         \ ||
+ tan\6      (xi + C)/ //

eq := (2*k*k)*w*beta*S-(2*alpha*k*k)*f-2*w*u[0]+k*u[0]*u[0];
/                /
|                |
|                |
1     |          (1/2) |
--------- |alpha (-6)      |
4320 beta |                |
\                \

/                        2\
/ (1/2)         \ |       / (1/2)         \ |  (1/2)
18 alpha tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ / 6
----------------------------------------------------------------
(1/2)
5 beta

2
/                        2\
(1/2) |       / (1/2)         \ |
27 alpha (-6)      \1 + tan\6      (xi + C)/ /
- ----------------------------------------------- -
(1/2)
10 beta

/                                       2 /
1      |             (1/2)    / (1/2)         \  |
----------- \27 alpha (-6)      tan\6      (xi + C)/  \1
(1/2)
5 beta

\\
||           /      /
2\\||           |      |
/ (1/2)         \ ||||      1    |      |
+ tan\6      (xi + C)/ //|| - ------- |alpha |
||   72 beta |      |
//           \      \

/                        2\
|       / (1/2)         \ |                /
9 alpha \1 + tan\6      (xi + C)/ /        1       |
----------------------------------- - ------------ \9 alpha
(1/2)                      (1/2)
5 beta                    20 beta

/                        2\
(1/2)    / (1/2)         \ |       / (1/2)         \ |
(-6)      tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ /

\\           /                /
\||           |                |          (1/2)
(1/2)|||      1    |          (1/2) |alpha (-6)
6     /|| - ------- |alpha (-6)      |---------------
||   30 beta |                |        (1/2)
//           \                \ 10 beta

(1/2)    / (1/2)         \
3 alpha 6      tan\6      (xi + C)/
+ -----------------------------------
(1/2)
10 beta

2\\                /
(1/2)    / (1/2)         \ ||                |
9 alpha (-6)      tan\6      (xi + C)/ ||        1       |
- ---------------------------------------|| + ------------ |
(1/2)              ||          (1/2) |
40 beta                   //   12 beta      \

/
|          (1/2)            (1/2)    / (1/2)         \
|alpha (-6)        3 alpha 6      tan\6      (xi + C)/
|--------------- + -----------------------------------
|        (1/2)                       (1/2)
\ 10 beta                     10 beta

2\  \
(1/2)    / (1/2)         \ |  |
9 alpha (-6)      tan\6      (xi + C)/ |  |
- ---------------------------------------|^2|
(1/2)              |  |
40 beta                   /  /
value(%);
/                /
|                |
|                |
1     |          (1/2) |
--------- |alpha (-6)      |
4320 beta |                |
\                \

/                        2\
/ (1/2)         \ |       / (1/2)         \ |  (1/2)
18 alpha tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ / 6
----------------------------------------------------------------
(1/2)
5 beta

2
/                        2\
(1/2) |       / (1/2)         \ |
27 alpha (-6)      \1 + tan\6      (xi + C)/ /
- ----------------------------------------------- -
(1/2)
10 beta

/                                       2 /
1      |             (1/2)    / (1/2)         \  |
----------- \27 alpha (-6)      tan\6      (xi + C)/  \1
(1/2)
5 beta

\\
||           /      /
2\\||           |      |
/ (1/2)         \ ||||      1    |      |
+ tan\6      (xi + C)/ //|| - ------- |alpha |
||   72 beta |      |
//           \      \

/                        2\
|       / (1/2)         \ |                /
9 alpha \1 + tan\6      (xi + C)/ /        1       |
----------------------------------- - ------------ \9 alpha
(1/2)                      (1/2)
5 beta                    20 beta

/                        2\
(1/2)    / (1/2)         \ |       / (1/2)         \ |
(-6)      tan\6      (xi + C)/ \1 + tan\6      (xi + C)/ /

\\           /                /
\||           |                |          (1/2)
(1/2)|||      1    |          (1/2) |alpha (-6)
6     /|| - ------- |alpha (-6)      |---------------
||   30 beta |                |        (1/2)
//           \                \ 10 beta

(1/2)    / (1/2)         \
3 alpha 6      tan\6      (xi + C)/
+ -----------------------------------
(1/2)
10 beta

2\\                /
(1/2)    / (1/2)         \ ||                |
9 alpha (-6)      tan\6      (xi + C)/ ||        1       |
- ---------------------------------------|| + ------------ |
(1/2)              ||          (1/2) |
40 beta                   //   12 beta      \

/
|          (1/2)            (1/2)    / (1/2)         \
|alpha (-6)        3 alpha 6      tan\6      (xi + C)/
|--------------- + -----------------------------------
|        (1/2)                       (1/2)
\ 10 beta                     10 beta

2\  \
(1/2)    / (1/2)         \ |  |
9 alpha (-6)      tan\6      (xi + C)/ |  |
- ---------------------------------------|^2|
(1/2)              |  |
40 beta                   /  /
simplify(%);
/       /
1                  |     2 |        / (1/2)
----------------------------------- \alpha  \24 I sin\6      (xi
4
(3/2)    / (1/2)         \
640 beta      cos\6      (xi + C)/

3                          4
\    / (1/2)         \          / (1/2)         \
+ C)/ cos\6      (xi + C)/  - 21 cos\6      (xi + C)/

/ (1/2)         \    / (1/2)         \
- 16 I sin\6      (xi + C)/ cos\6      (xi + C)/

2    \\
/ (1/2)         \     ||
+ 26 cos\6      (xi + C)/  - 9//

## Maple 2018.2 is not compatible with macOS Catalina...

Hi everybody

l I tried to install Maple 2018.2 on the golden master of Catalina and it didn't work : the installation process ended after the entering of the password to authorize the installation. In fact Maple 2018.2 still contains 32 bit elements. Is there a solution ? Thank you

David

## How to create a procedure that only uses x-points ...

Say you have your data, a list of coordinates as,

d1 := [[3, 11], [4, 6], [5, 8]]

Where the goal here is to take the x-coordinate, subtract that by two, then add all the subtracted coordinates together, basically,

(3-2)+(4-2)+(5-2) = 6

I would like to write a procedure to do this, my template done to the best of my maple knowledge below:

f2 :=proc(dat::list)

for i from 1 to nops(dat) do
val1:={{ PULL data[i,1]}}
sub2 :=val1-2

{{add sub2 to new 1 D array}}

end do;

{{sum array}}
end proc

The '{{ }}' brackets indicate that I have no idea how to do that function. Basically, I need to pull each x-element, subtract it by 2, add to a new list, and sum the list.

I would be grateful for any help, thanks!

## Which Bernstein has these result?...

Second terms coefficient = 2/3*x when (....)^2

9/16*x^2 when (...)^3

64/125*x^3 when (...)^4

625/1296*x^4

Which Bernstein has these result?

Which limit function of x^n = (n^(n-1))/((n+1)^(n-1))*x^(n-1)?

how to find and calculate?

## How to force axis labels in integers?...

I have a simple plot showing a quantity against another. The vertical axis values happen to be relatively large integers (tuning words for a direct digital synthesizer, if anyone cares). In the plot pasted-in below this would be W. Maple insists plotting these in scientific notation with 5 or so digits. Is there any way to force the vertical axis to show labels in integers? I scoured the docs for this but came up empty. To be clear, Maple does the right thing in 99% of all cases, is just that these tuning words are integers so the scientific expression makes no sense here. Plotting the equivalent Hex value would also be acceptable, except that I don't know how to do that either.

Thanks,

Mac Dude

## Getting an answer to display inline...

I have a dual boot mac book (so a mac book air with windows mode). I am trying to get my answer displayed inline (so the alt+enter on a normal windows computer), but I cant figure out how to do it on mine (since the alt+cmd+enter also doesnt work). Does someone have a solution for me?

## Help ! trying to fit assumed data values to a mode...

#I'm trying to fit data to a system equations with variables and parameters but couldnt run through.

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