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?
To solve a system of linear ODEs, you can use techniques such as substitution, elimination, or matrix methods. These methods involve manipulating the equations to isolate one variable at a time until you can solve for each variable.
The purpose of solving a system of linear ODEs is to find the solution that satisfies all of the equations in the system. This allows us to model and understand complex systems that involve multiple variables and their rates of change.
Yes, it is possible to have multiple solutions for a system of linear ODEs. This can happen when the equations are not independent, meaning that they can be simplified or combined to create the same solution.
Yes, numerical methods such as Euler's method, Runge-Kutta method, or finite difference methods can be used to solve a system of linear ODEs. These methods involve approximating the solution by using small intervals and calculating the values at each interval.
Yes, there are many real-world applications of solving systems of linear ODEs, such as modeling population growth, chemical reactions, and electrical circuits. It is also used in fields such as physics, engineering, and economics to understand and predict the behavior of complex systems.