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Hi!! i am working on assignment.

h:= x-> (x^17-x*sin(x^16))/x^49+exp(sqrt(x+8))*ln(abs((cos^4*(x)-5)));


i want to find the value of the h(10)

i use eval , but it comes out a function, not a solution.!!

I'm trying to solve a fourth order ODE but for some reason I only end up with three constants at the end. I'm using Maple 16. Here's the code I have been using:

dsolve(diff(x(t), t$4)+4*diff(x(t), t$2)-4*x(t)+1);

The output is 

x(t) = 1/4+_C1*exp(sqrt(-2+2*sqrt(2))*t)+_C2*exp(-sqrt(-2+2*sqrt(2))*t)+_C3*exp(-I*sqrt(2+2*sqrt(2))*t)

When I try to solve the homogeneous equation I get the expected four linearly indep solutions:

x(t) = _C1*exp(-sqrt(-2+2*sqrt(2))*t)+_C2*exp(sqrt(-2+2*sqrt(2))*t)+_C3*exp(-I*sqrt(2+2*sqrt(2))*t)+_C4*exp(sqrt(-2+2*sqrt(2))*t)

Adding 1/4 to this gives me the general solution I would expect, but I don't see why I should need to do this step. I'm at a loss for what I am doing wrong so any help would be greatly appreciated. Thanks in advance.





Vectors are defined by a lenth and an angle.

The arrow command wants me to give it a starting point and an endpoint in coordinates, for example:



gu := arrow([5, 10], [15, 20], .2, .4, .1, color = green)

I'm dealing with vectors from electrical circuits, so the information I have would be the lenth of the vector, and an angle given in degrees (which I could convert to radians if needed for the plot).

The goal is to plot all the vectors in the circuit on the same display so that it can be seen how they are in relation to each other, and to visualise the solution. This means I would need to find out the endpoint of the arrows to start the next arrow at that location with its angle in reference to the same axis. Does it make sence? I'm not sure about the wording of this.

Here's a picture of a calculated vector lenth and angle:

So, the -45 degrees would need to be in reference to the y-axis for example, then the next vector can be placed at lets say perpendicular in reference to the vector sol_1, starting at its endpoint.

The only other way I have to draw this, excluding doing it by hand, is using the object tools from microsoft word, and to be honset I dislike using word for math stuff. I would much rather learn the syntax for Maple to do this.


I hope someone knows what I mean, Please ask if somethig is unclear,








how to plot exp(f)*erf(g) where f and g are complex function


del from -100e-15 to 100e-15



Population at point A is 500. Point B 200. See pics.

where is the best point to meet such that the total distance is minimized. Can only go "taxi way", no diagonals allowed.

[the answer is (5,5).

Solution given: sumPop/2=~7 units. Left-right sum7 occurs at C, x=5. Bottom-top sum7 occurs at B, y=5].

there must be a better (Maple) way...

Are comma's ever used in denominators?

Just curious, since when say transcribing code from a book and you're in the denominator pushing the comma should automatically move you over and up to where one should be placed.  Not that it really matters but if it's easy to implement that would be a luxury (unless of course commas are used in denominators).

I am creating a plot but the numbers on the horizontal axis overlap.  Is there a way to change the directions of the numbers displayed under the horizontal axis (tickmark labels) from horizontal to vertical?

The picture below shows how the numbers are bunched together under the horizontal axis.  I'd like them to be displayed vertical



Thank you

1. Take a group for example. First we can set up a group G by

G:=<<a,b>|<a2=1,b3=1,(a.b)2=1>>. Actually,G=S3. So how to simplify a long production,

such as "a.b.b.a.b.b.a.b"?

2. How to define a finitely presented algebra over some field, such as the enveloping algebra

or quantum group of a Lie algebra? And moreover how to do the similar computation about 

simplifying a long production?


Anyone could help me in solving the following system of equations to get constants C1, C2, C3 and C4. MALPE give me this "soution may have been lost".  The MAPLE sheet is also attached.



Eq1:=simplify(C3*exp(-(1/4)*(C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)+C4*exp((1/4)*(-C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)-U) = 0;

C3*exp(-(1/4)*(C2*x^2+(x^4*(4*M*w1+C2))^(1/2))/w1)+C4*exp(-(1/4)*(C2*x^2-(x^4*(4*M*w1+C2))^(1/2))/w1)-U = 0


Eq2:=simplify(exp(-(1/4)*(C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C3*x+exp((1/4)*(-C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C4*x+C2-V-z) = 0;

exp(-(1/4)*(C2+(C2^2+4*M*w1)^(1/2))*x^2/w1)*C3*x+exp(-(1/4)*(C2-(C2^2+4*M*w1)^(1/2))*x^2/w1)*C4*x+C2-V-z = 0


Eq3:=simplify((-2*w2*w5*ln(C3*exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5))-C4)*sqrt(w2*w4*(w2*w4+w3*w6))+w2*w5*(-w2*w4+sqrt(w2*w4*(w2*w4+w3*w6)))*ln(exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5)))+C1*w3*w6*sqrt(w2*w4*(w2*w4+w3*w6)))/(sqrt(w2*w4*(w2*w4+w3*w6))*w3*w6)-1)= 0;

(-ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*w2^2*w4*w5+C1*w3*w6*(w2*w4*(w2*w4+w3*w6))^(1/2)-2*w2*w5*ln(C3*exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-C4)*(w2*w4*(w2*w4+w3*w6))^(1/2)+ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*(w2*w4*(w2*w4+w3*w6))^(1/2)*w2*w5-(w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6)/((w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6) = 0


Eq4:= simplify((-C2*x^2*w2*w4-.50*C2*x^2*w3*w6+sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-1.0*sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2/(w2*w4*w5))-2*C3*exp(-.5*sqrt(w2^2*w4^2+w2*w3*w4*w6)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6)) = 0;

(-C2*x^2*w2*w4-.5000000000*C2*x^2*w3*w6+(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-2.*C3*exp(-.5*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6) = 0


solve({Eq1, Eq2, Eq3,Eq4}, {C1, C2, C3,C4});

Warning, solutions may have been lost







Hi all,

I have this system

> system1D := H = alpha*gamma[2, 2]*d[2, 1]-beta*d[1, 2]*gamma[1, 2]^2-gamma*d[1, 2]*gamma[2, 1]^2+alpha*gamma[2, 2]^2*d[2, 2]-beta*d[2, 2]*gamma[2, 2]^2-gamma*d[2, 2]*gamma[2, 2]^2, E = alpha*gamma[2, 1]*d[1, 1]-beta*d[1, 2]*gamma[1, 1]-gamma*d[1, 1]*gamma[2, 1]+alpha*gamma[2, 1]^2*d[1, 2]-beta*d[2, 2]*gamma[2, 1]-gamma*d[2, 1]*gamma[2, 2], B = alpha*gamma[1, 1]*d[2, 1]-beta*d[1, 1]*gamma[1, 1]^2-gamma*d[1, 1]*gamma[1, 1]^2+alpha*gamma[1, 1]^2*d[2, 2]-beta*d[2, 1]*gamma[2, 1]^2-gamma*d[2, 1]*gamma[1, 2]^2, D = alpha*gamma[1, 2]*d[2, 1]-beta*d[1, 1]*gamma[1, 2]^2-gamma*d[1, 2]*gamma[1, 1]^2+alpha*gamma[1, 2]^2*d[2, 2]-beta*d[2, 1]*gamma[2, 2]^2-gamma*d[2, 2]*gamma[1, 2]^2, A = alpha*gamma[1, 1]*d[1, 1]-beta*d[1, 1]*gamma[1, 1]-gamma*d[1, 1]*gamma[1, 1]+alpha*gamma[1, 1]^2*d[1, 2]-beta*d[2, 1]*gamma[2, 1]-gamma*d[2, 1]*gamma[1, 2], C = alpha*gamma[1, 2]*d[1, 1]-beta*d[1, 1]*gamma[1, 2]-gamma*d[1, 2]*gamma[1, 1]+alpha*gamma[1, 2]^2*d[1, 2]-beta*d[2, 1]*gamma[2, 2]-gamma*d[2, 2]*gamma[1, 2], F = alpha*gamma[2, 1]*d[2, 1]-beta*d[1, 2]*gamma[1, 1]^2-gamma*d[1, 1]*gamma[2, 1]^2+alpha*gamma[2, 1]^2*d[2, 2]-beta*d[2, 2]*gamma[2, 1]^2-gamma*d[2, 1]*gamma[2, 2]^2, G = alpha*gamma[2, 2]*d[1, 1]-beta*d[1, 2]*gamma[1, 2]-gamma*d[1, 2]*gamma[2, 1]+alpha*gamma[2, 2]^2*d[1, 2]-beta*d[2, 2]*gamma[2, 2]-gamma*d[2, 2]*gamma[2, 2], H = alpha*delta[2, 2]*d[2, 1]-beta*d[1, 2]*delta[1, 2]^2-gamma*d[1, 2]*delta[2, 1]^2+alpha*delta[2, 2]^2*d[2, 2]-beta*d[2, 2]*delta[2, 2]^2-gamma*d[2, 2]*delta[2, 2]^2, E = alpha*delta[2, 1]*d[1, 1]-beta*d[1, 2]*delta[1, 1]-gamma*d[1, 1]*delta[2, 1]+alpha*delta[2, 1]^2*d[1, 2]-beta*d[2, 2]*delta[2, 1]-gamma*d[2, 1]*delta[2, 2], B = alpha*delta[1, 1]*d[2, 1]-beta*d[1, 1]*delta[1, 1]^2-gamma*d[1, 1]*delta[1, 1]^2+alpha*delta[1, 1]^2*d[2, 2]-beta*d[2, 1]*delta[2, 1]^2-gamma*d[2, 1]*delta[1, 2]^2, D = alpha*delta[1, 2]*d[2, 1]-beta*d[1, 1]*delta[1, 2]^2-gamma*d[1, 2]*delta[1, 1]^2+alpha*delta[1, 2]^2*d[2, 2]-beta*d[2, 1]*delta[2, 2]^2-gamma*d[2, 2]*delta[1, 2]^2, A = alpha*delta[1, 1]*d[1, 1]-beta*d[1, 1]*delta[1, 1]-gamma*d[1, 1]*delta[1, 1]+alpha*delta[1, 1]^2*d[1, 2]-beta*d[2, 1]*delta[2, 1]-gamma*d[2, 1]*delta[1, 2], C = alpha*delta[1, 2]*d[1, 1]-beta*d[1, 1]*delta[1, 2]-gamma*d[1, 2]*delta[1, 1]+alpha*delta[1, 2]^2*d[1, 2]-beta*d[2, 1]*delta[2, 2]-gamma*d[2, 2]*delta[1, 2], F = alpha*delta[2, 1]*d[2, 1]-beta*d[1, 2]*delta[1, 1]^2-gamma*d[1, 1]*delta[2, 1]^2+alpha*delta[2, 1]^2*d[2, 2]-beta*d[2, 2]*delta[2, 1]^2-gamma*d[2, 1]*delta[2, 2]^2, G = alpha*delta[2, 2]*d[1, 1]-beta*d[1, 2]*delta[1, 2]-gamma*d[1, 2]*delta[2, 1]+alpha*delta[2, 2]^2*d[1, 2]-beta*d[2, 2]*delta[2, 2]-gamma*d[2, 2]*delta[2, 2];

> subs({A = 0, B = 0, C = 0, D = 0, E = 0, F = 0, G = 0, H = 0, delta[1, 1] = 1, delta[1, 2] = 0, delta[2, 1] = 0, delta[2, 2] = 0, gamma[1, 1] = 1, gamma[1, 2] = 0, gamma[2, 1] = 0, gamma[2, 2] = 0, delta[1, 1]^2 = 0, delta[1, 2]^2 = 0, delta[2, 1]^2 = 1, delta[2, 2]^2 = 0, gamma[1, 1]^2 = 0, gamma[1, 2]^2 = 1, gamma[2, 1]^2 = 0, gamma[2, 2]^2 = 0}, {system1D});

The problem is: there is any simple way to use command "subs" when some expression such that delta[1,1]=1, gamma[1,1]=1, gamma[1,2]^2=1 have value and others are zero.

Can someone please advice and help me on this?



Hello to you all,

I have this DE

but when I try to change the variable

I get this

>algsubs(r(t) = 1/u(t), diff(diff(r(t), t), t)-k/r(t) = -K/r(t)^2);

Why is it not done for the rest of the terms.  Is there a more easy way to do it.  Take into account that I cannot use dsolve because it is in an course in integral.


Thank in advance for your help.


Mario Lemelin
Maple 2015 Ubuntu 14.04 - 64 bits
Maple 2015 Win 10 Pro - 64 bits messagerie : téléphone :  (819) 376-0987

Does anyone know an easy way to convert %d_ to D? I tried the convert command, but no effect.  Thanks.




For my lecture advanced dynamics, I got the question to make a sketch of the coordinate system and the particle’s motion, with the following position vector:

r(t) = (a cos(ωt))i + (b sin(ωt))j + (ct)k

In this function, ω is in [rad/s], a and b are in [m], t in [s] and c is [m/s].

I have no idea what this should look like, and I was thinking about plotting this with Maple, but thus far I'm not succeeding in plotting it. Which function or method can I use to visualize this in Maple?

Thanks a lot!


Hi all,

I have this system

> system2hD := 0 = -d[1, 2], 0 = -d[2, 1], 0 = -delta*d[1, 2], 0 = -d[1, 1]-delta*d[1, 1], 0 = -delta*d[1, 1]-d[2, 2];
> solve({system2hD, delta <> 0, delta <> 1}, {d[1, 1], d[1, 2], d[2, 1], d[2, 2]});
      {d[1, 1] = 0, d[1, 2] = 0, d[2, 1] = 0, d[2, 2] = 0}

But, I hope to get the answers as {d[1, 1] = -delta*d[1, 1], d[1, 2] = 0, d[2, 1] = 0, d[2, 2] = -delta*d[1, 1]}. I think, I should not use the command "solve".

Can someone please advice and hepl me on this?



Hello all,

Yesterday, I upgraded to Mac OS X El Capitan.

Now, when working with Maple 2015, I feel the gui is very slow and sometimes irresponsive, when trying to scroll through my worksheets as well as through help pages (e.g., "help plot3d"). When I do the same within Maple 18, it works without any problems.

Does anybody else have the same issue?



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