How do you solve for f in the differential equation (x^2-a^2)f'+xf=0?

  • Thread starter Helios
  • Start date
In summary, "A DE, maybe easy" is a type of mathematical equation that describes changes in a quantity over time or with respect to other variables. Solving DEs allows for understanding and predicting the behavior of systems and processes in various fields. The difficulty of solving DEs depends on the specific equation and techniques used. DEs have many applications, such as modeling population growth and optimizing systems. While a basic understanding of calculus and algebra is necessary, there are resources available for individuals with varying levels of mathematical background to learn about DEs.
  • #1
Helios
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This one looks easy but I don't know.

( x[tex]^{2}[/tex] - a[tex]^{2}[/tex] )f' + xf = 0
 
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  • #2
Isn't that separable?
 
  • #3
Rearrange to get

[tex]\frac{f^{\prime}}{f} = - \frac{x}{x^2 - a^2} [/tex]

now integrate to get

[tex]\ln{f} = -\frac{1}{2} \ln{(x^2 - a^2)} + C [/tex]
 

FAQ: How do you solve for f in the differential equation (x^2-a^2)f'+xf=0?

What is "A DE, maybe easy"?

"A DE, maybe easy" is short for "A Differential Equation, maybe easy." It is a type of mathematical equation that describes how a quantity changes over time or with respect to other variables.

What is the purpose of solving a DE?

The purpose of solving a DE is to understand and predict the behavior of a system or process. DEs are used in a wide range of fields, including physics, biology, economics, and engineering.

Are DEs difficult to solve?

It depends on the specific DE and the techniques used to solve it. Some DEs can be solved analytically with well-known methods, while others require numerical methods or advanced mathematical techniques.

What are some common applications of DEs?

DEs are used to model and understand a variety of real-world phenomena, such as population growth, chemical reactions, heat transfer, and electrical circuits. They are also used in optimization problems and control systems.

Do I need a strong background in math to understand DEs?

A basic understanding of calculus and algebra is necessary to understand and solve DEs. However, there are many resources available, such as textbooks and online tutorials, that can help individuals with varying levels of mathematical background to learn about DEs.

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