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Question: there is anyway for plot system of ode equation?

Question: there is anyway for plot system of ode equation?

Math-dashti 15 Maple 2024
ode homework differential-equations plotting stability
June 09 2025
2

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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