Which method should be used to solve this D.E.?

  • Thread starter Jeff12341234
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In summary, when determining which method to use for solving an equation, it is important to check if the equation has a form that is easy to solve, such as linear, exact, or separable. One should start by rewriting the equation and then check for separability, which is one of the easier methods to determine. If the equation is not separable, it is best to move on to other methods.
  • #1
Jeff12341234
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ex2=t-1ex2-[itex]\frac{1}{tx}[/itex][itex]\frac{dt}{dx}[/itex]

Which method should be used and how can you tell just by looking at it?
 
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  • #2
you check if the equation has a form that is easy to solve: linear, exact, separable, some others that are more difficult...

So, you start by rewriting the equation:
[itex] \frac{dt}{dx}=xe^{x^2}(1-t)[/itex]

It is linear as well as separable.
 
  • #3
To add to what bigfooted said, checking the equation for separability is one of the easier things to do, so that's one of the things you should do first.

If it turns out that an equation isn't separable, at least you haven't spend much time in checking.
 

1. What is a differential equation?

A differential equation (D.E.) is a mathematical equation that relates a function to its derivatives. It is used to describe the relationship between a quantity and its rate of change.

2. What are the different methods for solving a D.E.?

There are several methods for solving a D.E., including separation of variables, integrating factors, substitution, and power series. The choice of method depends on the type of D.E. and its complexity.

3. How do I know which method to use?

The method used to solve a D.E. depends on its type and complexity. Some D.E.s can be solved using more than one method. It is important to understand the characteristics of each method and choose the one that best suits the given equation.

4. Can a computer program be used to solve a D.E.?

Yes, there are many computer programs and software packages available that can solve D.E.s. These programs use numerical methods to approximate the solution and can handle complex and nonlinear equations.

5. Are there any real-world applications of solving D.E.s?

Yes, D.E.s are used in many fields of science and engineering to model and understand natural phenomena. They are used to study population growth, heat transfer, motion of objects, and many other real-world problems.

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