Items tagged with equation


A pirate ship is persuing a merchant ship when a fog descends, obscuring the merchant ship in front. What path must the pirate ship take to guarantee intercepting the other ship? [the pirate ship can go 5x faster than the merchant, and the merchant can move in any direction as long as it's in a straight line].

ok, so the pirate needs to move in a straight line for a little bit, then move in an ever increasing spiral, a logarithmic spiral. r=a.e^(b.theta) and in parametric form x(t)=a.e^(b.t).cos(t), y(t)=a.e^(b.t).sin(t)

So im asking if there is an underlying ODE and if Maple can derive the above equations (and the numbers a and b).

the tv show i got this from displayed the following eq: t=d/(v1+v2).e^(theta/sqrt((v1/v2)^2-1))

BTW if you're an internet troll reading this, and don't believe this question belongs on this forum, other members might disagree.


Here we develop the factoring in common factor, simple and complete square blade, plus simple equation systems with graphic and design, and graphic solution of the quadratic equation using components in maple 2015.

(in spanish)





If there is  an equation or are several equations, I need to obtain all the roots, how can I do???


fsolve ? rootfindings? or what?


If an examples of actual is given,  That will be perfect  !!!



hi guys , i have this warning for solving a complicated equation with 7 parameters. how can i overcome to this warning ?


odesys := {(1/4)*(-4*r^(2+p+a)*p*a-11*r^(2+a+c)*a*c-4*r^(2+p+c)*p*c+22*r^(2+a+n)*a*n+8*r^(2+p+n)*p*n-22*r^(2+a+c)*a+8*r^(2+p+a)*p-8*r^(2+p+c)*p+22*r^(2+b)*b+32*r^(2+p)*p^2+32*r^(2+p)*p+22*r^(2+b)*b^2+22*r^(2+2*a)*a+65*r^(2+2*a)*a^2-8*r^(2+p+c)*p^2+8*r^(2+p+a)*p^2-22*r^(2+a+c)*a^2)/r^4+(1/4)*(4*r^(a+n)*n^2-2*r^(n+c)*n*c-4*r^(n+c)*n^2+3*r^(2*n)*n^2-4*r^(a+c)*c+8*r^(a+n)*n+4*r^(2*c)*c-8*r^(n+c)*n+4*r^m*m^2-4*r^d*d+8*r^m*m+4*r^m-4*r^d)/r^2}



res := op(odesys);



SOL1 := solve(identity(res = 0, r), {a, b, c, d, m, n, p})

Warning, solutions may have been lost





guys, i have this equation which a, n, c, phi[0] are parameters and r is variable. maple solved this equation with n=0,c=c,phi[0]=5/4-1/4 c but i obtained another solution for this equation : a = 1, c = 5, n = 1, phi[0] = 1 ( you can check). 



odesys := {5*r^a+4*n-c*r^n-4*phi[0]}



res := op(odesys);




SOL := solve(identity(res = 0, r), [a, n, c, phi[0]]);

[[a = 0, n = 0, c = c, phi[0] = 5/4-(1/4)*c]]



eval(5*r^a+4*n-c*r^n-4*phi[0], [a = 1, c = 5, n = 1, phi[0] = 1])




how can i get all solutions for a equation like this ?


hi guys ,


i have two set equations and i want to solve them.



thanks guys

Is it possible to somehow extract a derivative from numeric solution of partial differential equation?

I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.

The actual problem i have is that i have to take a numeric solution, calculate a derivative from it and later use it somewhere else, but the solution that i have is just a set of numbers an array of some sort and i can't really do that because obviously i will get a zero each time.

Perhaps there is a way to interpolate this numeric solution somehow?

I found that someone asked a similar question earlier but i couldn't find an answer for it.

Hello everyoene, please i have a problem solving this delay differential equation:

y'(x)=cos(x)+y(y(x)-2)    0<x<=10

y(x)=1      x<=0


please i need the solution urgently

guys ,

in a differential equation i want to expand its variable, but i  have some problem with it for exponential term



thanks guys



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


can anybody help me? i want to check the consistency of my scheme. My equation is too long if i check manually, so i used maple 13 to simplify my equation. But it cannot simplify it because of length of output exceed limit 1000000


eqn1 := u+(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2)+(u-(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2))-u-(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)-u+(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3))*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3));



a := simplify(eqn1);

`[Length of output exceeds limit of 1000000]`





i want to find the stability of this equation, but there is seem to have some problems..can somebody help me..


y := A*(1/x+x*exp(-2*sqrt(-1)*b))+4*(exp(h)-1)^2*(2*exp(-sqrt(-1)*b)-3*(exp(h)-1)^2*x^(-exp(h)+1)*exp(sqrt(-1)*b*(-exp(h)+1-1))+3*x^(-exp(h)+1)*exp(sqrt(-1)*b*(-exp(h)+1-1)))/(3*(1-r))-exp(-2*sqrt(-1)*b)/x-x;

subs(A = (1+r)/(1-r), %);

subs(r = (1/3)*(exp(h)-1)^2, %);

subs(b = m*Pi*(exp(h)-1), %);

subs(m = 1, %);

subs(h = 0.5e-1, %);

> ans := solve(%, x);
Warning, solutions may have been lost

> r1 := ans[1];
Error, invalid subscript selector
> r2 := ans[2];
Error, invalid subscript selector

Any suggestions (or perhaps related examples?) illustrating how I might numerically solve for f(t) in the following non-linear integral equation?  In Fortran, I would start with a guess f(t)=T0, and then search in the neighborhood for a minimum (in the error), but I am not familiar with numerical searches and methods in Maple.  Thank you for any suggestions or leads.

(a,b,... etc are all real)

T__0 := 298.

`&Delta;T` := 25.

0 < beta and beta <= 1


f*t = T[0]+`&Delta;T`*[1-exp(-a(int(exp(-b/f(y)), y = y[1] .. t))^beta)]






How to find (i. e. to evaluate) the positive root of the polynomial equation

mul(x+j, j = 0 .. 2015)=1?

The command

RootFinding:-NextZero(x-> mul(x+j, j = 0 .. 2015)-1 , 0);


The same with Digits:=100.

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.

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