Items tagged with exp

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.



Dear all,

I have a question: how to compute the roots of exp(z) = -1 with z in C? 

I tried: 

fsolve( exp(z) = -1, z, complex );

But it only gives one root (0.1671148658e-3+4.934802220*10^9*I) which does not even seem to be correct. I would prefere smth like z_n = I*(2*n-1)*pi or at least multiple roots...

By using

solve(exp(x) = -1, x);

it returns I*Pi.


MATLAB MuPAD gives the desired result:

solve(exp(x) = -1, x)

(PI*I + 2*PI*k*I, k in Z)




Hello! Hope every is fine. I want to expand all expression of exp of the attached file like this

exp(c[1]*t+d[1]*n-d) = exp(c[1]*t+d[1]*n)*exp(-d)

waiting your kind response.



Mob #: 0086-13001903838


I assume that I'm not providing the correct input to the simplify command to get the simplification that I want.  In particular, for the following code:

assume(n, positive);

The expression should evaluate to 0.  However, the first expression does not simplify to 0 (it does not simplify at all in Maple) while the second expression simplifies to 0.

The simplification is fairly easy for the first expression by factoring 6 and combining terms; it seems like I'm not entering the command to simplify in this way.

After manually working out answer for problem 4-4 in Mathews & Walker's Mathematical Methods of Physics , I tried to check my solution with maple2015. Briefly the problem involves inputs periodic with period T, being transformed into outputs, through a kernal G.  The net result is that all input frequencies omega periodic in T are multiplied by (omega_0/omega)^2, except for constant frequency which transforms to zero.  The problem asks to evaluate the kernal G.

Maple2015 correctly evaluated the integral for a constant input, a cosine input, and a sine input, but gave undefined when I tried an exponential(i*x) input which is just a linear combination of the two previous inputs.  I found this interesting because the integral is finite, well defined, and only has an absolute function (in the kernal), which may cause Maple problems, as it correctly evaluated integral when I split it into two regions.  Interestingly if instead of working with a period of T, I used 2*pi, and redfined my G function accordingly, Maple evaluated the exp input integral without any problems.  So the problem appears to be with the T variable, but I correctly used assumptions of T>0, and 0<t<T, so I am not sure why it would work correctly when I use T=2*pi, but failed when using a general period T.  Any help would be welcome.




assume(T > 0)

assume(0 < t and t < T)


Originally T, renamed T~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: real
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)



Originally t, renamed t~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: RealRange(Open(0),infinity)
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)


assume(n::integer, n > 0)


Originally n, renamed n~:

  is assumed to be: AndProp(integer,RealRange(1,infinity))


G := proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc

proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc


(int(G(t-tp), tp = 0 .. T))/T



(int(G(t-tp)*sin(2*Pi*n*tp/T), tp = 0 .. T))/T



(int(G(t-tp)*cos(2*Pi*n*tp/T), tp = 0 .. T))/T



(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. T))/T



(int(G(t-tp)*(cos(2*Pi*n*tp/T)+I*sin(2*Pi*n*tp/T)), tp = 0 .. T))/T



simplify((int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. t))/T+(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = t .. T))/T)



assume(0 < t and t < 2*Pi)

G2 := proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc

proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc


(int(G2(t-tp)*exp(I*n*tp), tp = 0 .. 2*Pi))/(2*Pi)







Hello! Hope every is fine. I want to expand the following expression



like this 


i.e., expand exp(2*c*t+2*d*n-d) into exp(2*c*t+2*d*n)*exp(-d) 

waiting your kind response 

M := 10^2; plot(exp(M), t);

When we execute the above code we get graph in output naturally. But when execute the following code  , there is no graph in output, why?

M := 10^3; plot(exp(M), t);

Thanks in advance for any suggestion.

I am trying to integrate product of exp(t+s) and a piecewise polynomial but the result can not be read and not usefull. also I used numerical integration function "Quadrature" but the result did not change.


I got the Real and Imaginary of an expression J1 




J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)


but when I change the expression  for J1 to be



J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help


It seems a frequent issue that exported 3d plots are not shown as wished. I experience the same problem. Although I exported in the .eps format into a .tex latex-file the resulting .pdf-file shows a somewhat pixelated image of my 3d plot as if it was created in "Paint". Is there a solution for this in Maple13?

I'm trying to get the RHL of exp1:=(2/(1+e^(-1/x)) as x->0+

and have l2:=limit(exp1,x=0,right) but that isn't giving me a value. How do I correct this? 


Hi all.

I try to get the real part from the complex expression. But it turns out to not be the simplest result:


convert(exp(-I*k[0]*h), sin);


Maple results in:


while the simplified result should be:



I wander how to get the simplifyed result in maple. Thanks

AOA... How are you all. I need the answer of the following question.


input in Maple: expand(exp(a+b)+exp(c+b))

output:  exp(a)*exp(b)+exp(c)*exp(b)


input in Maple: expand(exp(2a+b)+exp(3c+b))

output:  (exp(a))^2*exp(b)+(exp(c))^3*exp(b)

but i need exp(2a)*exp(b)+exp(3c)*exp(b)


PhD (Scholar)
Department of Mathematics

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation


is there a faster way to calculate exp(x) than with the x^k/k! series












Is it possible to plot WKB solutions such as exp(-I*f(x)*x)/sqrt(f(x); where f(x) is any generic function of x e.g. sin^2x ? I have been trying in maple but can't get it to give me a plot.

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