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when solving a system of equations, I want to get rid of all the absolute functions.


for example, |y-2|=x,I don't want maple solve this equation directly...because maple may has difficulties when dealing with absolute values. Instead, I want to transform this equation by squaring the both sides at the same time which end up this equation: (y-2)^2=x^2.


The example I provide is kind of simple...what if there are multiple absolute term in the equations? Is there a general way to get what I need? Or Is it practical to use Maple to achive such thing?


thanks in advance.

solve 30a+75b+110c+85d+255e+160f+15g+12h+120i=8000 over the positive integers

solve 30a+75b+110c+85d+255e+160f+15g+12h+120i=800000 over the positive integers


I know there are two branches for the lambertw function meet my demand.

I wonder whether there is a method to find the _Z2 value with SS::real, for the above commands, they are 0&-1.

thank you for any advice.

Hi, I'm trying to solve a system of equation and I keep getting this error. Could anyone help me figure out what I'm doing wrong?

My problem is:

> alpha := .3; G := 3.5; L := 6; f := 1.1;

for i to 50 do

I0 := x(z)+y[i](z); ICon := x(0) = 1, y[i](0) = 0;

for j to 50 do

i <> j;

d1 := diff(x(z), z) = -G*x(z)*y[i](z)/IC-alpha*x(z);

d2 := diff(y[i](z), z) = G*y[i](z)*y[j](z)/IC-alpha*y[i](z);

dsys := {d1, d2};

F := dsolve({ICon, op(dsys)}, [x(z), y[i](z)], numeric);

end do;

end do;
Error, (in dsolve/numeric/process_input) unknown y[2] present in ODE system is not a specified dependent variable or evaluatable procedure


Hello! I'm really craving for a piece of advice from you pros.
For simplicity's sake let's start with this made-up system.



Here is solver options with pair of events to get idea about what I want.

Plot of solution

For my purposes it's essential to restrict variables m and D(fi1)(t), D(fi2)(t). While it's very convenient to use piecewise() operator in first case with m, I simply can't find working method for second.

I've tried various events for dsolve, but they trigger only once and I failed to provide continuous restriction on the derivatives in question.

That's what I need in the end:

If there's a way to obtain this result, please, don't make secrets of it :) Thank you in advance!

I input:

solve({My(x, -(1/2)*b) = 0, My(x, (1/2)*b) = 0, w(x, -(1/2)*b) = 0, w(x, (1/2)*b) = 0}, {Am, Bm, Cm, Dm});

and recieved: 

Error, (in My) invalid input: diff received -1, which is not valid for its 2nd argument


My is 

My := proc (x, y) options operator, arrow; -((1/2)*I)*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x-y)/a))^2/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^3*a^2)+I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x+y)/a))^2/((exp(Pi*(I*x+y)/a)-1)^3*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x+y)/a))^2/((exp(Pi*(I*x+y)/a)-1)^3*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))^2*a^2)-((1/2)*I)*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a^2)-((1/2)*I)*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Dm*(exp((2*I)*Pi*x/a)-1)*Pi*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a)+I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x-y)/a))^2/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^3*a^2)+I*Dm*(exp((2*I)*Pi*x/a)-1)*Pi*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a)-((1/2)*I)*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+sum(-4*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(d(y), y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+32*(diff(po(y), y))*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))/(Pi(y)^7*m(y)^7*d(y))-56*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-56*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-8*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+32*po(y)*a(y)^3*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(a(y), y))/(Pi(y)^7*m(y)^7*d(y))+16*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(a(y), y), y))/(Pi(y)^7*m(y)^7*d(y))-56*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-56*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-8*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)-224*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-224*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-32*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+392*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))*(diff(m(y), y))/(Pi(y)^8*m(y)^8*d(y))+56*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))*(diff(d(y), y))/(Pi(y)^8*m(y)^7*d(y)^2)+56*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))*(diff(d(y), y))/(Pi(y)^7*m(y)^8*d(y)^2)+4*(diff(diff(po(y), y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))+8*(diff(po(y), y))*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))+4*po(y)*a(y)^4*(2*(diff(Pi(y), y))^2*m(y)^2*y(y)^2+8*Pi(y)*m(y)*y(y)^2*(diff(Pi(y), y))*(diff(m(y), y))+8*Pi(y)*m(y)^2*y(y)*(diff(Pi(y), y))*(diff(y(y), y))+2*Pi(y)*m(y)^2*y(y)^2*(diff(diff(Pi(y), y), y))+2*Pi(y)^2*(diff(m(y), y))^2*y(y)^2+8*Pi(y)^2*m(y)*y(y)*(diff(m(y), y))*(diff(y(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(diff(m(y), y), y))+2*Pi(y)^2*m(y)^2*(diff(y(y), y))^2+2*Pi(y)^2*m(y)^2*y(y)*(diff(diff(y(y), y), y))+8*(diff(a(y), y))^2+8*a(y)*(diff(diff(a(y), y), y)))*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))-28*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(m(y), y), y))/(Pi(y)^7*m(y)^8*d(y))+48*po(y)*a(y)^2*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))^2/(Pi(y)^7*m(y)^7*d(y))+224*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))^2/(Pi(y)^9*m(y)^7*d(y))+224*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))^2/(Pi(y)^7*m(y)^9*d(y))+8*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(d(y), y))^2/(Pi(y)^7*m(y)^7*d(y)^3)-28*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(Pi(y), y), y))/(Pi(y)^8*m(y)^7*d(y)), m = 1 .. infinity) end proc;

[Lengthy, poorly formatted, and very-difficult-to-read plaintext prettyprint of the above procedure removed by a moderator.--Carl Love]

Dear all;

Thank you very much for helping me to understand this problem.

I need your help for this question, it's seem for correct but when I run the code there is no dispaly of the solution with this command  dsolve({ode,ics}) ;





dsolve({ode,ics}) ;

Is there any some kind of environment variable(or command,package, anything...) that I can play with to tell maple consider all the constrants implied by the given expression


For Example, I want to simplify the following equation(this equation's final form is "0=0" if you take the implied constraints into account.)

 "(4*a^3*b)^(1/2)/(-(a/(4*b))^(1/2))+(4*a^3*b*(4*b/a))^(1/2) = 0" 

in real domain and this equation implies that variable a and b are both negative or positive because of the sqrt operation. And neither a nor b should be zero because they are part of a fraction's denominator.

but if i simply tell maple to simplify this equation, all the constrants will be ignored by maple, even if i use RealDomain package.

the following cmd gives me three 3 solutions: -1, 1,sqrt(2), even if I specificlly assume that a is not equal to neither 1 or -1....

([RealDomain[solve]((1/(a-1)-1/(a+1))*(2*a^2-2)/a = 4/surd(2, 2), useassumptions = true)] assuming a <> 1, a <> -1


why does this wired thing happen?

hi, the equations read as 

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three some time,some solutions are lost,the result show  me  random.may i have run the command serveral times? regards.

Hi there,


I am trying to compute the following, and I am getting this error.


> A := map(convert, M, unit_free)*Unit('m'*(1/'s'^2));
(I had to put the Unit('m'*(1/'s'^2)) because the original units were kNm/s^2 (kg), and even though I simplified it, it's still using kNm/s^2, and leaves the m/s^2 for some reason when I try to remove the units. I tried simply changing the units on the original matrix, but the units menu has disappeared from the right-click menu!!)

> B := map(convert, K, unit_free);


Loading RealDomain;


Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'should not happen: Rename expects the input to contain unknown functions'

Why is it giving me this error? omega is an unknown variable that I am trying to solve for. I am going a modal analysis, so maybe there is a better way to find omega?


Any help appreciated!



I want to  get   nonlinear equations solutions using 'solve',but i always meet that the program running long long time,i want to stop this 'solve' procedure giving a limit do i.can you help me.thanks a lot.

Why does Maple 2015 solve this very simple system incorrectly?

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});



With Maple 12 no problem:

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});




Can I use Maple to solve equation like |a-b|+\sqrt{2b+c}+c^2-c+1/4=0 for a,b,c?


a,b,c are real numbers and I need to solve it in real domain.

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