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Hello people in the mapleprimes,

I have a question, so I hope someone give me answers to it.

I calculated for the solution of the follwing differential equation.

b:=diff(y(x),x)+a*y(x)=f(x);#where a and f(x) is not specified.

subs({f(x)=exp(x),a=2},%);where f(x) and a are specified.


The solution of the above was

y(x) = (1/3)*exp(x)+_C1/(exp(x))^2,  (A)

where please note that the second term takes

the form of fraction _C/(exp(x))^2.


On the other hand, next I calculated the following differential equation where f(x) and a are specified from the start.




y(x) = (1/3)*exp(x)+exp(-2*x)*_C1  (B)

was the obtained solution.


Each (A) and (B) are the same substantially mathematically. But, for Maple, the variable powered to minus brabra

is not the same as one over variable powered to brabra, so that (A) and (B) takes different forms, and maple will see them 

different with each other.


  Surely, with algsubs, algsubs(_C1/(exp(x))^2=exp(-2*x)*_C1,c) transforms (A) to (B).

But, I want to know whether there are some other ways than that  to modify (A) to (B).

If there are any good ways for it, I will be happy if you teach them to me.

Thanks in advance.



How can I simplify $\sqrt{1−r^2\exp(2i\theta)}$ in Maple. I could do it by hand but I need this type of simplification later for far more complicated expressions.  I allready tried to enter this as a complex number using II, but simplify(...,'symbolic') didn't simplify this expression. Any suggestion?

Hi everybody

In the following attached file that is a simple code, 2 problems occur:

1- The values of Lc1 and Lc2 are specified in the third and fourth lines of the code. when I execute Pcl10, Maple does not replace Lc1 with its value that is 0.5*L. This problem does not happen for Tcl10 and Tcl21. Why Maple does not replace Lc1 with its value that is specified at the start of the worksheet?

2- In the last line, when I try to simplify the Tcl10, Maple returns an error, while for example the first element i.e. Tcl20(1,1) can be simplified as: cos(thet1+thet2). What is the source of error?


Thanks in advance

I am curious, can simplify/siderels be executed in mod p by some equivalent Maple function call?

I am trying to simplify the square of a parameterized polynomial mod 2. My parameters are intended to be either 0 or 1. How do I accomplish this?

For example:


alias(alpha = RootOf(x^4+x+1))



z := alpha^3*a[3]+alpha^2*a[2]+alpha*a[1]+a[0]``



z2 := collect(`mod`(Expand(z^2), 2), alpha)








I would like to simplify the squared parameters modulo 2. a[3]^2=a[3], etc.

Any help would be appreciated. Elegant methods even more so!






i use the pdsolve to find the solutions of a system of partial differential equations,

but the result contains some indefinite integrals, how to simplify it further?

thank you


eq1 := {6*(diff(_xi[t](x, t, u), u))-3*(diff(_xi[x](x, t, u), u)), 12*(diff(_xi[t](x, t, u), u, u))-6*(diff(_xi[x](x, t, u), u, u)), 2*(diff(_xi[t](x, t, u), u, u, u))-(diff(_xi[x](x, t, u), u, u, u)), diff(_eta[u](x, t, u), t)+diff(_eta[u](x, t, u), x, x, x)+(diff(_eta[u](x, t, u), x))*u, 18*(diff(_xi[t](x, t, u), x, u))+3*(diff(_eta[u](x, t, u), u, u))-9*(diff(_xi[x](x, t, u), x, u)), 6*(diff(_xi[t](x, t, u), x, x))+3*(diff(_eta[u](x, t, u), x, u))-3*(diff(_xi[x](x, t, u), x, x)), 6*(diff(_xi[t](x, t, u), x, u, u))+diff(_eta[u](x, t, u), u, u, u)-3*(diff(_xi[x](x, t, u), x, u, u)), 12*(diff(_xi[t](x, t, u), u))-6*(diff(_xi[x](x, t, u), u))+6*(diff(_xi[t](x, t, u), x, x, u))-6*(diff(_xi[t](x, t, u), u))*u+3*u*(diff(_xi[x](x, t, u), u))-3*(diff(_xi[x](x, t, u), x, x, u))+3*(diff(_eta[u](x, t, u), x, u, u)), 12*(diff(_xi[t](x, t, u), x))-6*(diff(_xi[x](x, t, u), x))+2*(diff(_xi[t](x, t, u), t))+2*(diff(_xi[t](x, t, u), x, x, x))-4*(diff(_xi[t](x, t, u), x))*u+2*(diff(_xi[x](x, t, u), x))*u+_eta[u](x, t, u)-(diff(_xi[x](x, t, u), t))+3*(diff(_eta[u](x, t, u), x, x, u))-(diff(_xi[x](x, t, u), x, x, x))};



Dear all

I have such an expression in the file ( Obviously it is not a simple form. 10should be cancelled both in denominator and nominator. I have applied the function simplify(). However, it doesn't work.  I hope someone can do me a favor. That will help me a lot. Thanks

I know that the following expression (a:=6*s*sqrt(9*s^2+32)+18*s^2+32)

can be rewritten as

However, none of the following maple functions is abble to give the factored result:




Someone could help me to understand what is going on, please?

I was trying to make a function (or procedure) that uses the simplify command and outputed all the different types of simplify that are in the right click menu.  I never know which one to chose so until I get the hang of what they are, I wanted to see all of them at once.  Can someone set me off on the right path?


I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison := (-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1]+(-sin(a(t))*sin(g(t))*sin(b(t))+cos(a(t))*cos(g(t)))*xb[1]+sin(a(t))*cos(b(t))*yb[1]+(sin(a(t))*sin(b(t))*cos(g(t))+cos(a(t))*sin(g(t)))*zb[1]+x(t)-xp(t) = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :


I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

I attached the code 


Thank you for your help


I have a complex equation EQ, it gives me 4 answers - two complex, one negative and one positive. Which assumptions do i need to use to automatically get one answer - real and positive one?

I tried similary to what I did with real equations:
simplify(solve(EQ)) assuming real, positive
But that didn't work


is there a way to substitute funktion combinations when they have the same arguments? I want to substitute abs(exp)*abs(1,exp) with exp. Algsubs works as long as I know the excat expressions. However, I want to do this substitution for any exp. Simplify doen't work here ether.

I also tried to write my own simplification rule with no success:




abs(a)*abs(1, a)



{abs(x)*abs(1, x) = x}


simplify(f,siderel);    #expected result: a

abs(a)*abs(1, a)








Thanks in advance!

Dear maple users,

I have a lengthy formulation of function f(x) which contains some constant coefficients (A1, A2, A3 ...). I would like to simplify f(x) for functions of same above mentioned coefficients as following:

f(x) = f1(x) A1 + f2(x) A2 + ... + fn(x) An

I tried the following command:

collect(simplify(f(x)), [A1, A2, A3 ...])

Maple returns the expected form of functions but the problem is that Maple did not simplify f1(x), f2(x)... Obviously, I do not want to simplify manually : simplify(f1(x)) ... again

How can I solve this problem?


Can Maple simplify these DE's by eliminating the d/dt VL(t) by taking the derrivative of the bottom equation and substituting in the first one? 

In this question, I asked for a way to simplify an expression containing radicals. The discussion led us to that as default field for simplicfication is the Complex number system we should use assume or assuming command to simplify the radicals. However, the mothod suggested there seems to not work in this new case that I have. For details please see the attached file. The terms sqrt{u} and sqrt{u-1} should cancel in denominator.

 What Maple Does


`ϕ` := (1+sqrt(5))*(1/2)



f := (1/2)*sqrt(-(u-1)*(u+1)*(u^2-u-1))*u*(4*u-3)/sqrt(u*(u-1))



`assuming`([combine(f)], [1 < u and u < `&varphi;`])



`assuming`([simplify(f)], [1 < u and u < `&varphi;`])



`assuming`([combine(f, radical)], [1 < u and u < `&varphi;`])



`assuming`([simplify(f, radical)], [1 < u and u < `&varphi;`])




 Remark by Markiyan Hirnyk. The below content is added by the questionner on 08.02.2016 .

What Mathematica Does


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