How to solve a complex differential equation using the chain rule?

In summary, a complex differential equation is a mathematical equation involving complex numbers and derivatives used to model systems with real and imaginary components. It differs from a regular differential equation as it includes complex numbers, and can be used in various applications such as physics and engineering. Solving a complex differential equation involves finding a function that satisfies the equation using techniques like separation of variables or numerical methods. Common techniques for analyzing complex differential equations include finding solutions, stability analysis, and phase plane analysis.
  • #1
newcool
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From a physics problem I obtained this differential equation.
[tex]\frac{d^3x}{dt^3} =-2(\frac{dx}{dt})^3[/tex]

Would appreciate any tips on how to solve it as I have no idea on how to start.Thanks for the help
 
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  • #2
Ugh! Hint: try multiplying both sides by [tex] \frac{d^2 x}{dt^2} [/tex] and see what you can do.
 
  • #3
[tex]1 =-2\frac{d^2 x}{dt^2}*(\frac{dx}{dt})^2[/tex] ??

I have only covered up to integration in calculus.
 
  • #4
Just use the chain rule. For example, what is [tex] \frac{d}{dt}\left( \frac{1}{2} \left(\frac{d^2 x}{dt^2} \right)^2 \right) \,\,?[/tex]
 

1. What is a complex differential equation?

A complex differential equation is a mathematical equation that involves both complex numbers and derivatives of a function. It is typically used to model physical systems that exhibit behavior involving both real and imaginary components.

2. How is a complex differential equation different from a regular differential equation?

A complex differential equation is different from a regular differential equation in that it involves complex numbers, whereas a regular differential equation only involves real numbers. This means that the solutions to a complex differential equation will have both real and imaginary components, while the solutions to a regular differential equation will only have real components.

3. What are some applications of complex differential equations?

Complex differential equations have many applications in physics, engineering, and other fields. They are commonly used to model systems involving electrical circuits, fluid dynamics, and quantum mechanics.

4. How do you solve a complex differential equation?

Solving a complex differential equation involves finding the function that satisfies the equation. This can be done using various techniques, such as separation of variables, power series, or numerical methods. In some cases, a complex differential equation may not have an exact solution, and approximate solutions must be found.

5. What are some common techniques for analyzing complex differential equations?

Some common techniques for analyzing complex differential equations include finding exact or approximate solutions, stability analysis, and phase plane analysis. These techniques can help determine the behavior and properties of solutions to the differential equation.

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