Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance. 

123.mw

Hi, I have an homework where I need to find the highest point and the lowest point on an ellipse form by the intersection of two equations wich are 4x-3y+8z=5 and z^2=x^2+y^2 and I have to use the LagrangeMultiplier command. I get how it works but I can't get the correct form. How should I do it ? 

restart;
Pr:=0.71: n:=-1:

eta0:=0.0699;

EQ1:=diff(H(x), x ) - x*diff(F(x), x ) ;
 

EQ2:=(1+x^2)*diff(F(x), x$2) + (3*x + x*F(x)-H(x))*diff(F(x), x) + F(x)^2 + G(x)^2 +2*P(x) + x*diff(P(x), x) ;

EQ3:=(1+x^2)*diff(G(x), x$2) + (3*x + x*F(x)-H(x))*diff(G(x), x) ;

EQ4:=(1+x^2)*diff(H(x), x$2) + (3*x + x*F(x)-H(x))*diff(H(x), x) + (1+F(x))*H(x)- diff(P(x), x);

EQ5:=(1+x^2)*diff(theta(x), x$2) + x*(1-2*n)*diff(theta(x), x) + n^2*theta(x) - Pr*( n*F(x)*theta(x) + ( H(x)-x*F(x) )*diff(theta(x), x)  ) ;

EQ:={EQ1=0, EQ2=0,EQ3=0,EQ4=0 ,EQ5=0}:

IC:={ F(0)=0, G(0)=12, H(0)=0, theta(0)= 1, F(eta0)=0, G(eta0)=12, H(eta0)=0, theta(eta0)= 0, P(0)=0};
 

sol:= dsolve(EQ union IC,numeric,output=Array([0,0.0699]));

ques.mw

Just wanted to ask, what the issue here is:

restart;
Int(1/(1 - x*ln(x)), x);
IntegrationTools:-Change(%,u=1-x*ln(x),u);

doesn't give the proper transformation. It gives

Int(1/u,u)

Solving for x and writing the transformation in terms of LambertW gives something else, if I'm not mistaken.

I cannot view 3d graphics with my version of Ubuntu 20.04. I've updated all my computer's graphics card drivers and the problem persists. If I run without hardware acceleration, nothing changes; no visualization and no production possible.
Do you have any ideas for solving this problem? Maple uses OpenGL libraries for 3D production and visualization, and these libraries are installed on my computer. Would installing mesa solve the problem, for example?

Thanks in advance.