Hi. I have solved numerical an ODE and want to use the solution in the integrand of a subsequent integral. I'm being frustrated by my lack of knowledge and the internet isn't helping! I hope someone can put me right.....here's the relevant part of code.

dsysA := {diff(r(s), s) = sqrt((g*r(s) + h)^2 - 1 + 1/r(s)), r(0) = rinit};
dsnA := dsolve(dsysA, numeric, abserr = 10^(-6));

dsnA(0.1);
               [s = 0.1, r(s) = 1.51303353884965]

rA := s -> rhs(dsnA(s)[2]):

rA(0.2);
                        1.53235325247661

tA := s -> tinit + int((g*rA(p) + h)/(1 - 1/rA(p)), p = 0 .. s):

tA(0.01);
Error, (in rA) invalid input: rhs received dsnA(p)[2], which is not valid for its 1st argument, expr
 

Hi, I want to minimize a*x + log2(3+4.2^(-x)+2^(-2x)) , x>0 & 0<=a<=1 where a is some constant. Is there any command in maple which help me to minimize this. For command minimize, I am unable to minimize the function symbolically. I need to minimize it in terms of a.

Hi I am trying to compute the series approximation for the difference between these two divergent integrals

M := int(cosh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x));

N := int((1 + x)*sinh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x))

where x,p are positive and x is approaching zero. I would like to get a series expansion of M-N, but I am not quite if this is possible.

Dear Users!
Hope everyone fine here. I have a vector V and want a new vector after transformation like

V := Vector(5, {(1) = 2, (2) = 3, (3) = -1, (4) = 9, (5) = 7});

after square transformation of V I got a new vector W like bellow

W := Vector(5, {(1) = 4, (2) = 9, (3) = 1, (4) = 81, (5) = 49});

and similarly sin transformation of V give the following matrix as

U := Vector(5, {(1) = sin(2), (2) = sin(3), (3) = sin(-1), (4) = sin(9), (5) = sin(7)});
Please help me to get vectors W and U.

Dear all
Using cubic spline interpolation to interpolate a given function I get  
the follwoing error
Warning, solving for expressions other than names or functions is not recommended.
Error, (in solve) list of unknowns contains repeated elements: [1, 0]

and  why the  spline funciton obtained by this code is different to the one given by Maple's built in package.

inter.mw

Thank you for any help 

I want to remove the term XY
f:=(x,y)->2*x²+xy+y²+4x-y-2=0;
eq := simplify(subs(x = X-9/7, y = Y+8/7, f(x, y)));
theta:=Pi/8;
ex := simplify(subs(X = cos(theta)*X-sin(theta)*Y, Y = sin(theta)*X+cos(theta)*Y, eq)); evalf(%);
How to obtain (3+sqrt(2))/2*X²+(3-sqrt(2))/2=36 ? Thank you.

Hello,

I have two ordiary differential equations to be solved numerically. One of the equations can be solved independently (no need to solve the 2nd differential equation). However, in order to solve the 2nd differential equation, I need the numerical solution from the 1st one. 

sol1:=dsolve({ode1,x(0)=x__0, D(x)(0)=x__1},numeric, x(t), parameters=[a,b,c])

sol1(parameters=[4,5,1])

Now, I need to solve the 2nd differential equation which will give me y(t), but the differential equation depends on the function of x(t). What is the syntax of dsolve which incorporates the solution of another differential equation?

Hello, 

How one would define a function of a function-- a functional?

Given

f(g(r)) := int(g(r), r)

I would like to get 

int(h(r+eps),r)

when I call it like

f(h(r+eps))

I could achieve this behaviour by substitions, but is there a nicer and shorter way of doing this?

Thanks in advance.

I am trying to solve this equation, I tried
 

restart; 
ListTools[Categorize]; 
L := []; 
for a to 20 do
 for b to 20 do 
for c to 20 do 
for d to 20 do 
for e to 20 do 
for f to 20 do 
for g to 20 do 
for h to 20 do 
if sqrt(a+b*sqrt(c+d*sqrt(e +f*sqrt(g)))) = h then L := [op(L), [a, b, c, d, e, f, g, h]] end if
 end do end do end do end do end do end do end do end do; nops(L)

where g is not a square of a integer number . I do not get any solutions for a long time. How to reduce timing to solve this equation?

 

In this code, there are 8 vectors, each vector has 5 points except vectors 7 and 8 with 4 points. I made their  (7 and 8) respective fifth point a string. However, this error statement pops up "Error, invalid input: log[10] expects its 1st argument, x, to be of type algebraic, but received 2.51E-10".

Can someone help me with the correction?

Thank you all and kind regards

restart;

B:=<<601,1201,2401,4801,9601>|<2.87E-19,7.94E-21,7.94E-23,1.03E-24,5.91E-26>|
    <2001,4001,8001,16001,32001>|<3.30E-2,5.37E-4,8.47E-6,1.33E-7,2.08E-9>|
    <183,365,728,1476,2910>|<4.58E0,7.54E-8,2.20E-11,4.95E-14,9.15E-15>|
    <1621,3020,6166,12022,"2222">|<2.95E-3,8.51E-6,3.39E-8,2.51E-10,"2.51E-10">>:

for i from 1 to 5 do
   B[i, 2] := log[10](B[i, 2]):                      
   B[i, 4] := log[10](B[i, 4]):         
   B[i, 6] := log[10](B[i, 6]):         
   B[i, 8] := log[10](B[i, 8]):

   B[i, 1] := log[10](B[i, 1]):                      
   B[i, 3] := log[10](B[i, 3]):         
   B[i, 5] := log[10](B[i, 5]):         
   B[i, 7] := log[10](B[i, 7]):

end do:  # computing the log of the max-error
B: # This is the table of values we'll plot.

T:=plot([B[..,[1, 2]],B[1..1,[1, 2]], B[.., [3, 4]],B[1..1,[3, 4]], 
     B[..,[5, 6]],B[1..1,[5, 6]],B[.., [7, 8]],B[1..1,[7, 8]]], 
    legend = ["","BFFM","", "BNM","", "BHM","", "ARKN"],
    #title="Efficiency Curve for Example 5",
    style = ["pointline","point","pointline","point","pointline","point","pointline","point"], 
    symbolsize = 15,axes = framed, 
    symbol = [box,box, circle,circle,solidbox, solidbox,solidcircle, solidcircle],
    color=[ red, red, gold,gold, blue, blue,black, black], 
    axis = [gridlines = [colour = green, majorlines = 1,linestyle = dot]], 
    labels = [typeset(log__10(`NFE`)), typeset(log__10(`Max Err`))]);

This question came to me when I answered in this thread  https://www.mapleprimes.com/questions/231603-Solve-Onevariable-Equation

The equation there is quite cumbersome, I extracted a shorter subexpression from it (I converted all floats to exact constants), but the  solve  command hangs when trying to solve it. fsolve  handles the equation easily. We can see that the equation  Eq  is quite simple and easy to solve even by hand. I ask this question in a separate topic, because this seems to be a serious bug in the  solve  command.

restart;
Eq:=1-1/(1+203808*exp(-342569/506*t)*(1/131537))^(131537/203808)=44983/56599;
solve(Eq);

Edit. I noticed that the  isolate  command solves the problem, but of course the question remains open with  solve .

Hi, 
 

Trying to change the color of the plot that Statistics:-Sunflower produces is not trivial:

restart:
interface(version);
Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895

# This example comes from the help page
with(Statistics):
data := Vector[row]([2, 5.3, 4.6, .88, 2.5, 5.9, 5, 10, 1.7, 7.8, 7.2, 9.42, 9.01, 3.42, 4, 11.59, 8, 10.3, 1.5, 8.5, 11.4]):
a := SunflowerPlot(data, length = 4, size = [600,200], color=red):
a;     # navy blue plot
op(a); # look at the structure of a to see why red is not accounted for

After having examined the structure of 'a', I circumvent this problem by doing this:

b1 := SunflowerPlot(data, length = 4, size = [600,200]):  #no more color specified
c  := op(select(has, op(1, b1), COLOUR));
b2 := eval(b1, c=COLOUR(RGB, 1, 0, 0)):

# Red sunflowers!!!
plots:-display(b2)  

Does it exist a simpler way to set the color of the sunflowers through some option of  Statistics:-Sunflower ?

TIA

Hello,

I have the following function:

y:=t->808.2213240*(1 - 0.63*(1993551437/1601983488 - sqrt(3)/2)^0.3)*(1 - 335345*(45188/147189 - 53/(4820*ln(2)))*335345^(131537/203808)*131537^(72271/203808)*(1 - 1/(1 + (203808*exp(-677.0138344*t))/131537)^(131537/203808))/34603964738)

I want to solve for t when y(t)=196.9594856. I tried solve(y(t)=196.9594856,t) and it took several minutes of still evaluating before I gave up. Any ideas? Cheers.

Hi,

I am looking to convert two expressions into to one, however, their arguments are supposed to be numerically in order:

For my procedure, I need them in order, namely

-1,-1, -0.415862444399209580898770761551,0.425609408597783496007437773936,1

Is it possible to do this with expressions without having to convert them to a list? Since my following code expects expressions, and not lists, I wouldn't like to change the whole program around it.

The order in which expressions evaluate in Maple is something that occasionally causes even advanced users to make syntax errors.

I recently saw a single line of Maple code that provided a good example of a command not evaluating in the order the user desired.

The command in question (after calling with(plots):) was

animate(display, [arrow(<cos(t), sin(t)>)], t = 0 .. 2*Pi)

This resulted in the error:

Error, (in plots/arrow) invalid input: plottools:-arrow expects its 3rd argument, pv, to be of type {Vector, list, vector, complexcons, realcons}, but received 0.5000000000e-1*(cos(t)^2+sin(t)^2)^(1/2)
 

This error indicates that the issue in the animation is the arrow command

arrow(<cos(t), sin(t)>)

on its own, the above command would give the same error. However, the animate command takes values of t from 0 to 2*Pi and substitutes them in, so at first glance, you wouldn't expect the same error to occur.

What is happening is that the command 

arrow(<cos(t), sin(t)>)

in the animate expression is evaluating fully, BEFORE the call to animate is happening. This is due to Maple's automatic simplification (since if this expression contained large expressions, or the values were calculated from other function calls, that could be simplified down, you'd want that to happen first to prevent unneeded calculation time at each step).

So the question is how do we stop it evaluating ahead of time since that isn't what we want to happen in this case?

In order to do this we can use uneval quotes (the single quotes on the keyboard - not to be confused with the backticks). 

animate(display, ['arrow'(<cos(t), sin(t)>)], t = 0 .. 2*Pi)

By surrounding the arrow function call in the uneval quotes, the evaluation is delayed by a level, allowing the animate call to happen first so that each value of t is then substituted before the arrow command is called.

Maple_Evaluation_Order_Example.mw