Mathematica Help VectorPlot ODE - Need help

[pat666]

Homework Statement

Produce a graphical display of the solutions for the ode:
$$y''+8y'-9y=22e^(2t)$$

Homework Equations

The Attempt at a Solution

VectorPlot[{1, y'' + 8 y' - 9 y}, {x, -3, 3}, {y, -3, 3}] Doesn't seem to work, because it just gives me a graph of horizontal line. I know that that is not a graphical display of the solution, I will overlay ContourPlots of that once I figure out what's going on.

Thanks

 

[KataKoniK]

for sharing your attempt at a solution to this problem. The equation given is a second-order ordinary differential equation (ODE), which means it requires two initial conditions to find a unique solution. Therefore, a graphical display of the solution would require a specific set of initial conditions.

One possible approach to finding a graphical display of the solution would be to use a numerical method such as Euler's method or Runge-Kutta method to approximate the solution for various sets of initial conditions. This would result in a series of points that could be plotted on a graph, showing the behavior of the solution over time.

Another approach would be to use a computer algebra system or a programming language to solve the ODE symbolically for a range of initial conditions and plot the resulting solutions on a graph. This would provide a more precise and comprehensive graphical display of the solutions.

In any case, it is important to note that the graphical display of the solution will depend on the values chosen for the initial conditions, and may look different for different sets of initial conditions. It is also important to check the accuracy of the solution obtained, as numerical methods may introduce some error.

I hope this helps in your efforts to produce a graphical display of the solutions for this ODE. Good luck!