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How i can fix this issue ?...

Math-dashti 95 Maple 2024
ode homework differential-equations
June 28 2025
1 1

i want to plot the function appear in P but there is a variable t which appear from variable which my system is depending on u,v and must v appear in my function instead of exponential so exponential contain the t variable  there is any way for fixing this?

> 

restart;
> 

with(plots):

 

> 

f := (u,v) -> -u+u^3;
g := (u,v) -> -2*v;

proc (u, v) options operator, arrow; -u+u^3 end proc

  

proc (u, v) options operator, arrow; -2*v end proc

 (1)

 

> 

equilibria := solve({f(u,v)=0, g(u,v)=0}, {u,v});

{u = 0, v = 0}, {u = 1, v = 0}, {u = -1, v = 0}

 (2)

 

> 

de1 := diff(u(t),t) = f(u(t),v(t));
de2 := diff(v(t),t) = g(u(t),v(t));

diff(u(t), t) = -u(t)+u(t)^3

  

diff(v(t), t) = -2*v(t)

 (3)
   
> 

PDEtools:-ConservedCurrents({de1, de2}, [u(t), v(t)]); P1 := -(1/2)*op(1, rhs(op(%)))

[_J[t](t, u(t), v(t)) = f__1((-u(t)^2+1)*exp(-2*t)/u(t)^2, v(t)*exp(2*t))]

  

-(1/2)*(-u(t)^2+1)*exp(-2*t)/u(t)^2

 (4)
> 

P := -(-u^2+1)*exp(-2*t)/(2*u^2)

-(1/2)*(-u^2+1)*exp(-2*t)/u^2

 (5)

 

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equilibria;

{u = 0, v = 0}, {u = 1, v = 0}, {u = -1, v = 0}

 (6)

 

> 

p1 := contourplot(P, u=-1.5..2, v=-1.5..1.5, scaling=constrained,
    colorscheme="DivergeRainbow", contours=[seq](x, x=-0.4..0.4,0.1)):

Error, (in plot/iplot2d:-Levels) could not evaluate expression

  

 

> 

p2 := pointplot([[0,0],[1,0],[-1,0]], symbol=solidcircle, symbolsize=15, color=black):

 

> 

p3 := fieldplot([f(u,v), g(u,v)], u=-1.5..2, v=-1.5..1.5,
        arrows=medium, fieldstrength=fixed(0.4), grid=[10,10], labels=["",""]):

 

> 

display(p1,p2,p3, axes=normal);

 

  

Download p1-1.mw

can stability of one equation shown by ...

Math-dashti 95 Maple 2024
ode differential-equations plotting
June 27 2025
1 0

it is apear by sign of taking derivative from equation and substitute in it the sign less zero is stable otherwise is unstable but i want to shown by graph like shown in graph

plot-stablity-1equation.mw

How remove this sign Root0f- even use a...

Math-dashti 95 Maple 2024
solve implicit allvalues
June 27 2025
0 2

what is problem in here

> 

restart;
> 

with(plots):
> 

with(LinearAlgebra):
> 

with(DEtools):

diff(u(x), x) = f(u(x), v(x)), diff(v(x), x) = g(u(x), v(x)) for the two differential equations.

> 

f := (u,v) -> u+cos(v);
g := (u,v) -> u*v-v+sin(v);

proc (u, v) options operator, arrow; u+cos(v) end proc

  

proc (u, v) options operator, arrow; v*u-v+sin(v) end proc

 (1)

The equilibria:

> 

equilibria := solve({f(u,v)=0, g(u,v)=0}, {u,v},explicit);

{u = 1, v = Pi}, {u = -cos(RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z)), v = RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z)}

 (2)
> 

allvalues(RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z))

RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, 1.306542374), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, -1.306542374), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, -2.331122370), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, 2.331122370), 0

 (3)
 

NULL

Download remove.mw

How do the linearization of systems?...

Math-dashti 95 Maple 2024
ode differential-equations jacobian
June 27 2025
1 0

when we do the linearization we do transfer the critical point to the orgin, i want see the plot of nonlinear system before the linearization and after linearization which is critical point is tranfered to orgin, also i try to find `conserved quantity` and make a good plot with the critical point shown in graph how i can do the linearization by maple, also  we  by hand when we solved we show that in new system when we give him variable we have to write for each new system  u=x-x[0] when is u is new system for linearization we need that or not? becuase result is not change when we take jacobian result is same !

 

Linearization.mw

How plot matrix with C.Q?...

Math-dashti 95 Maple 2024
ode differential-equations phaseportrait
June 27 2025
0 0

i want plot a system of differential equation and do phaseportrait i did but when i want make it a little bit more clear and colorfull like rainbow when i find the C.Q i don't know how set the option for ploting?

e1.mw

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