The discussion revolves around solving a system of linear ordinary differential equations (ODEs) involving two unknown functions, \(x(t)\) and \(y(t)\). Participants explore strategies for finding solutions given a single equation that relates the derivatives of these functions.
Participants express differing views on the feasibility of solving for both functions simultaneously, with some agreeing on the limitations imposed by having only one equation. The discussion remains unresolved regarding the best approach to take in solving the system.
The discussion highlights the challenge of solving a system of equations with insufficient equations relative to the number of unknowns. There are references to external resources that may contain relevant information, but the specific assumptions and definitions used in the problem are not fully clarified.
kalish said:I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$
What is the best strategy?
chisigma said:You have two unknown function x(*) and y(*) and only one equation. That means that You can find x(*) as function of y(*) and y'(*) or vice versa, not both x(*) and y(*)...
Kind regards
$\chi$ $\sigma$
kalish said:$1.$ I solved for $U$.
$2.$ Then I solved the equation for $V$.
$3.$ Now I am plugging in the expression for $U$ into the equation for $V$ (because it looks easier than plugging in the other way around).
Shouldn't this give me a solvable equation for $V$, thus giving $V$, and then let me plug back into the main equation to get $U$??
Ackbach said:Could you please explain what $U$ and $V$ are? I think it'd also be terrific if you could please provide more context for this problem. How did this problem come to you? Is there any other information you have?