# Solving an ODE: Step-by-Step Guide and Tips

In summary, the order of an ODE is determined by the highest derivative present in the equation, and the general strategy for solving an ODE involves identifying its order and using integration techniques. Not all ODEs have analytical solutions, so it is important to check if the ODE is solvable by looking at its form. If an analytical solution cannot be found, a computer program can be used to solve the ODE numerically. To check the accuracy of a solution, it can be plugged back into the original equation or compared to known solutions.

## Homework Statement

$$(4x^3 p^2-2p)dx+(2x^4 p-x)dp=0$$

## The Attempt at a Solution

I have no idea how to solve it. It's not an exact differential and It's not of any famous ODE form that. Any ideas would be appreciated.

Last edited:
Problem was solved. sorry that I opened a thread for it. I just needed to factor out (x^3p-1).

## 1. How do I determine the order of an ODE?

The order of an ODE is determined by the highest derivative present in the equation. For example, if the equation contains only first derivatives, it is a first-order ODE. If it contains second derivatives, it is a second-order ODE, and so on.

## 2. What is the general strategy for solving an ODE?

The general strategy for solving an ODE involves first identifying its order and then using integration techniques to find a solution. This typically involves separating variables, integrating both sides, and applying initial conditions to determine any constants of integration.

## 3. How do I know if an ODE is solvable?

Not all ODEs have analytical solutions, so it is important to first check if the ODE is solvable. This can be done by looking at the form of the equation and determining if it falls into a known category of solvable ODEs, such as separable, homogeneous, or exact.

## 4. Can I use a computer program to solve an ODE?

Yes, there are many computer programs and software packages available that can solve ODEs numerically. These programs use algorithms to approximate the solution and can handle more complex ODEs that may not have analytical solutions.

## 5. How can I check if my solution to an ODE is correct?

One way to check the accuracy of an ODE solution is to plug it back into the original equation and see if it satisfies the equation. Additionally, you can compare your solution to known solutions or use a computer program to verify the solution.

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