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Hi all,


I tried to find the real solution of the unlinear integral equation:


exp(-h^2/T)*(Int(exp(-x^2/T)*BesselI(0, h*x/T)*x, x = 0 .. 1))/T


but I got the warning and an complex solution:


 solve(subs(T = 1, eq)-.99 = 0, h)

Warning, solutions may have been lost



Can anyone help me to find a real solution for this issue (if possible)...?

I would like to thank you in advance.


EF.3.mwHi, I want to ask that how to find the exact solution of equation without applying any technique

Dear Collegues

I have a system of odes as follows



Teq := N_bt*T(eta)^2*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(diff(T(eta), eta, eta))*gama1^2*b[k1]+N_bt*T(eta)^2*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))*(diff(T(eta), eta, eta))*gama1^2*a[k1]+2*N_bt*T(eta)*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(diff(T(eta), eta, eta))*gama1*b[k1]+N_bt*T(eta)^2*(diff(T(eta), eta, eta))*gama1^2;

UEQ:=(a[mu1]*(-(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta)))+(T(eta)-1)*gama1*(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta))^2))*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+2*b[mu1]*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(-(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta)))+(T(eta)-1)*gama1*(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta))^2)))*(diff(u(eta), eta))+(1+a[mu1]*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+b[mu1]*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2)*(diff(u(eta), eta, eta))+1-exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))*rhop/rhobf;

I want to solve them with the following boundary conditions

T(0)=0, T(1)=1

u(0)=L*D(u)(0), D(u)(1)=0

However I tried, I cannot find the solution in a closed form. I want to know that is there a closed form solution for the above odes?

Thank you



Im trying to study some questions and I'm using maple to verify my answers.

Theres a few polynomial factoring questions and linear equation questions Im trying to get

maple to show its solutions steps using showsolution() no matter where I put it  the function wont work.

Ive switched between math/text functions. Im still pretty new to maple but I can't find any information on how to do it

on the web/youtube.


Thanks in advance!

For the life of me I cannot find the method to do so.


So the solution would look like:

1. Euation

2 Step 2

3 Step 3

4 step 3+n

where n is the number of steps reuired.

Any help will be appreciated so very much.



Larry C



I'm not sure why im getting a complex solution for evalf(h(-1/2)). Posted screenshot here:

The answer should be positive 6*2^(2/3) ≈ 9.52

 The computer returns

h(-1/2) =


The problem is that evalf((-1)^(1/3)) you get 0.500 + .866I

Is there no way to evaluate a second derivative of a real valued function which has a fractional exponent without receiving complex results? I don't have the time to look at each function and try to figure out what went wrong. I want to plug in any x value into a function defined for all reals and get a real result.

I tried  assume(x , 'real' ) , that did not do anything.



Dear all,

I am trying to solve the following partial differential equation (transport or advection equation) with given initial and boundary conditions:

restart: with(PDEtools):
sys := [v*diff(u(x,t), x) + diff(u(x,t), t) = 0, u(x,0) = exp(-x), u(0,t) = sin(t)];

But it does not work. The solution is (or should be): 

u(x, t) = exp(t*v-x)+Heaviside(t-x/v)*(sin(t-x/v)-exp(t*v-x))

I think the reason is that the interval for t (in [0, inf)) and x (in [0, 1]) is not specified. On the other hand, this works:

restart: with(PDEtools):
sys := [diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x,0) = f(x)];
sol := pdsolve(sys);

How can I solve a PDE like the transport equation with given initial AND boundary conditions?

Thanks a lot


I'm having a problem with my student work, about to have a solution of 6 equations... Can help me in this file? i dont know how to solve this... this had-me a null solve...



Thanks for the help =)


M1 := 0.15e5;





















`σadm` := 175*10^6;







Atria := (3.5*12)/(LBC+LCD)



Ctria := LAB+LBC+(1/3)*(2*(LCD+LDE))



AiXil := Atria*Ctria



C := AiXil/Atria






SumFX := FAx;



SumFY := FAy+FCy+FEy-F5-QTria;



SumMA := FCy*(LAB+LBC)-F5*(LAB+LBC)+FEy*(LAB+LBC+LCD+LDE)+M1-MA-QTria*Ctria;






EIYac := EIYo+`EIθo`*x+M1*(x+0)^3/factorial(3);



EIYce := EIYac+FCy*(x-4)^3/factorial(3)-F5*(x-4)^3/factorial(3)-q5*(x-4)^5/((3.5)*factorial(5));



EIYef := EIYce+FEy*(x-7.5)^3/factorial(3)+(1/3)*q5*(x-7.5)^5/factorial(5);



`EIθac` := diff(EIYac, x);



`EIθce` := diff(EIYce, x);



`EIθef` := diff(EIYef, x);




Mac := diff(`EIθac`, x);



Mce := diff(`EIθce`, x);



Mef := diff(`EIθef`, x);




Vac := diff(Mac, x);



Vce := diff(Mce, x);



Vef := diff(Mef, x);




x := 0:

`EIθo` = 0


EIYo = 0


x := 4:



x := 7.5:



SOL := solve({CF1, CF2, CF3, CF4, SumFY, SumMA}, {EIyo, FAy, FCy, FEy, MA, `EIyθo`});








Hi, I have a function as following:


where d1=0.01..0.06, d2>=d1, d3>=d2, d4>=d3, a1>0,a2>0, a1+a2<0.6.

I want to get  all the solutions of d1,d2,d3,d4,a1,a2, which satify the equation and the constrains, is there any way to solve this problem by using maple?





This is the system of equations in term of sin and cos. I have used the command "solve" in Maple but it yielded only 2 solutions. I've tried to use with(RealDomain): It yielded more solutions but most of them were wrong.



f1 := -8100+(-30+70*cos(t1)-40*cos(t2))^2+(-70*sin(t1)+40*sin(t2))^2

f2 := (-20-80*cos(t3))^2+(-15+70*cos(t1)+10*cos(t1+t))^2+(-70*sin(t1)-10*sin(t1+t)+80*sin(t3))^2-5625

f3 := (-20-80*cos(t3))^2+(15+40*cos(t2)+10*cos(t1+t))^2+(-40*sin(t2)-10*sin(t1+t)+80*sin(t3))^2-5625

f4 := 10*cos(t1+t)*(30-70*cos(t1)+40*cos(t2))-10*sin(t1+t)*(70*sin(t1)-40*sin(t2))


Anybody know how to solve this system of equations to get the full set of roots?

Thank you very much in advance.

Int(piecewise(t < T1, exp((1/2)*t*(1+2*I-I*sqrt(3))), t < T2, -1000*exp((1/2)*t*(1+2*I-I*sqrt(3)))*(-1/1000+T1-t), T2 <= t, -1000*exp((1/2)*t*(1+2*I-I*sqrt(3)))*(-1/1000-T2+T1)), t)



Dear's, I am facing some problem to find the particular solution please find the attachment.


PhD (Scholar)
Department of Mathematics


please help check what's wrong with this code. I need the analytic solution and convert to Bessel but return error. Here is the worksheet

Best regards.

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

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}) ;

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