Weird differential equation

In summary, a weird differential equation is a type of differential equation that has unusual or unexpected behaviors, such as strange or non-continuous solutions. They are used in various scientific fields and have real-life applications, such as modeling chaotic systems and optimizing designs. Techniques for solving these equations include separation of variables, series solutions, and numerical methods, but exact solutions may not always be possible.
  • #1
Pachito
4
0
Hi everybody.
Not very good in solving DE's. Here is one for the better:

ay'+by = (y'+cy)^2+d

where a,b,c and d are real positive constants.

I know that : y(0)=0 and y''(0)=k*d (k= real positive constant)

Any possible suggestions?
Thanks
Pachito
 
Last edited:
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  • #2
I know that : y(0)=0 and y''(0)=k*d (k= real positive constant)
Two initial conditions are too much for a first oreder ODE. This implies a relationship between the coefficients of the ODE. If this relationship is not satisfied, no valid solution can be derived. See attachment :
 

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  • #3
Thank you very much for the illumination
 

1. What is a weird differential equation?

A weird differential equation is a type of differential equation that has unusual or unexpected behaviors. It may have strange solutions, multiple solutions, or solutions that cannot be expressed in terms of elementary functions.

2. What makes a differential equation "weird"?

A differential equation can be considered "weird" if it does not follow the usual patterns or behaviors observed in other types of differential equations. This can include unpredictable solutions, non-continuous solutions, or solutions that cannot be solved using traditional methods.

3. How are weird differential equations used in science?

Weird differential equations are used in various scientific fields, such as physics, biology, and engineering. They can be used to model complex systems and phenomena that cannot be described using simpler equations. They are also used in research to explore new mathematical concepts and theories.

4. Are there any real-life applications of weird differential equations?

Yes, there are many real-life applications of weird differential equations. For example, they can be used to model chaotic systems, such as weather patterns, population dynamics, and chemical reactions. They are also used in engineering to optimize designs and predict the behavior of complex systems.

5. Are there any techniques for solving weird differential equations?

There are various techniques for solving weird differential equations, depending on the specific equation and its behavior. Some common methods include separation of variables, series solutions, and numerical methods. In some cases, exact solutions may not be possible, and approximations or simulations may be used to understand the behavior of the equation.

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