# Trouble solving an ODE and plotting its phase portrait

• zeesyk
In summary, the conversation focused on solving a problem using Mathematica. The first part was solved by hand, resulting in a sideways parabola phase portrait. However, the individual wanted to also show this on Mathematica by solving the equation and plotting the phase portrait, but encountered difficulties. The mentor advised on the correct way to input the equation and mentioned that there was no need to specify the domain for DSolve."
zeesyk
Mentor note: Moved from non-homework forum to here hence no template.

So I was able to solve part 1.A of the first problem by hand, the phase portrait is a sideways parabola. However, I want to also show on this on mathematica. I want to solve the equation first and then plot the phase portrait it but this is what shows on my screen. What am I doing wrong?

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2) You have to write it like this: differential equation == 0. For example, if you had ##y'(t) = t## you should have written ##y'(t) - t = 0##.

3) DSolve should give the analytical solution so there is no need to specify the domain ({t, 0, 10}) you can just write t.

scottdave

## 1. How do I solve an ODE?

Solving an ODE involves finding a function that satisfies the given differential equation. This can be done analytically using techniques such as separation of variables, substitution, or integrating factors. Alternatively, numerical methods like Euler's method or Runge-Kutta methods can be used to approximate the solution.

## 2. What is a phase portrait?

A phase portrait is a graphical representation of the behavior of a dynamical system over time. It shows the relationship between different variables and their rates of change, and can help visualize the overall behavior of the system.

## 3. How do I plot a phase portrait?

To plot a phase portrait, you will need to first solve the ODE and obtain the equation for the solution. Then, choose a range of values for the variables and use them to plot a direction field. Finally, plot a few trajectories on the direction field to get a complete picture of the system's behavior.

## 4. What do the trajectories in a phase portrait represent?

The trajectories in a phase portrait represent the possible paths that a system can take over time, starting from different initial conditions. They can also indicate the stability of the system and any potential equilibrium points.

## 5. Can I use software to solve an ODE and plot its phase portrait?

Yes, there are many software programs available that can solve ODEs and plot phase portraits. Some popular options include MATLAB, Mathematica, and Python with the SciPy library. These programs can also handle more complex systems of ODEs and provide more detailed visualizations.

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