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Question: why solution changes when using dsolve with couples system?

Question:why solution changes when using dsolve with couples system?

nm 9718 Maple 2023
ode dsolve differential-equations
November 27 2023
2

I am really confused by this behavior. Should the solution be different when calling dsolve(ode) vs. dsolve(ode,[x(t),y(t)]) where here ode is list of two coupled first order ode's?

Maple shows the solutions in reverse order in one case vs. the other. I do not see why adding [x(t),y(t)] should make x(t) solution now y(t)'s and y(t) solution now x(t)'s.  Here is an example

Here is worksheet. I just find the out changing very confusing. Should not the same solution for x(t) and y(t) remain the same regardless of adding the second option as list of not? What is the logic behaind this change or order, and how it one to know which is the correct one as they look different.

``

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, October 25 2023 Build ID 1753458`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1592 and is the same as the version installed in this computer, created 2023, November 27, 3:41 hours Pacific Time.`

> 

restart;

20440

> 

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

[diff(x(t), t) = (3/2)*x(t)+2*y(t), diff(y(t), t) = (1/2)*x(t)+y(t)]

> 

simplify(dsolve(ode,[x(t),y(t)]));

{x(t) = -(1/2)*c__2*(17^(1/2)-1)*exp(-(1/4)*(-5+17^(1/2))*t)+(1/2)*c__1*exp((1/4)*(5+17^(1/2))*t)*(17^(1/2)+1), y(t) = c__1*exp((1/4)*(5+17^(1/2))*t)+c__2*exp(-(1/4)*(-5+17^(1/2))*t)}

> 

simplify(dsolve(ode));

{x(t) = c__1*exp((1/4)*(5+17^(1/2))*t)+c__2*exp(-(1/4)*(-5+17^(1/2))*t), y(t) = -(1/8)*c__2*(17^(1/2)+1)*exp(-(1/4)*(-5+17^(1/2))*t)+(1/8)*c__1*exp((1/4)*(5+17^(1/2))*t)*(17^(1/2)-1)}

> 

#when using SET instead of LIST, then same solutions come out as above
simplify(dsolve(ode,{x(t),y(t)}));

{x(t) = c__1*exp((1/4)*(5+17^(1/2))*t)+c__2*exp(-(1/4)*(-5+17^(1/2))*t), y(t) = -(1/8)*c__2*(17^(1/2)+1)*exp(-(1/4)*(-5+17^(1/2))*t)+(1/8)*c__1*exp((1/4)*(5+17^(1/2))*t)*(17^(1/2)-1)}

> 

 

Download why_solution_changes_nov_27_2023.mw
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