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Can plot the matrix instead of linear sy...

Math-dashti 120 Maple 2024
matrix ode homework
June 10 2025
2 4

in thus example all of them are write in shape of matrix but all of them are linear differential equation which have critical point zero ,i want to plot thus example and decided the kind of critical point by eagenvalue and by eagenvector i can find the trajectory how i can plot by matrix of each example and show that that critical point is which type as mention in picture?

system-phase-examples.mw

there is anyway for plot system of ode ...

Math-dashti 120 Maple 2024
ode homework differential-equations
June 09 2025
1 0

i want plot like that but i can't  and there is anyway for finding the equalibriom point of system? 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(DEtools)
> 

with(DynamicSystems)
> 

sys := {diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

{diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

 (1)
> 

fns := {x(t), y(t)}

{x(t), y(t)}

 (2)
> 

sol := dsolve(sys, fns)

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

 (3)
> 

ode := [diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]; S := dsolve(ode)

[diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]

  

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

 (4)
> 

Student:-ODEs:-ODESteps(ode, {x(t), y(t)})

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆt) x(t)=2 x(t)+3 y(t),(ⅆ)/(ⅆt) y(t)=2 x(t)+y(t)]],["•",,"Define vector"],[,,x(t)=[?]],["•",,"Convert system into a vector equation"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)+[?]],["•",,"System to solve"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)],["•",,"Define the coefficient matrix"],[,,A=[?]],["•",,"Rewrite the system as"],[,,(ⅆ)/(ⅆt) x(t)=A*x(t)],["•",,"To solve the system, find the eigenvalues and eigenvectors of" A],["•",,"Eigenpairs of" A],[,,[[-1,[?]],[4,[?]]]],["•",,"Consider eigenpair"],[,,[-1,RTABLE(18446744074191517278,MATRIX([[-1], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[1]=[]],["•",,"Consider eigenpair"],[,,[4,RTABLE(18446744074192645174,MATRIX([[3/2], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[2]=[]],["•",,"General solution to the system of ODEs"],[,,x=`c__1` (x)[1]+`c__2` (x)[2]],["•",,"Substitute solutions into the general solution"],[,,x=[]+[]],["•",,"Substitute in vector of dependent variables"],[,,[?]=[?]],["•",,"Solution to the system of ODEs"],[,,{x(t)=-`c__1` (e)^(-t)+(3 `c__2` (e)^(4 t))/2,y(t)=`c__1` (e)^(-t)+`c__2` (e)^(4 t)}]]"

 (5)
 

NULL

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