Very Tough Nonlinear First Order Differential Equation

In summary, the conversation discusses the difficulty of finding an analytic solution for the differential equation y' = a*(y^n) + c, where a, n, and c are constants. The conversation suggests using the power series method or factoring the equation into a separable form, but acknowledges that the resulting integral may be challenging to solve. It is mentioned that MATLAB may be able to compute a solution, but it is uncertain.
  • #1
sexycalibur
3
0
1. y' = a*(y^n) + c

a, n and c are constants. Any idea about this problem ? How can it be solved ?

i think there is no analytic solution

thanks for your help in advance
 
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  • #2
There are a couple of ways to solve this; power series method if you only need to solve to a specified power. Otherwise use the fact that the diff eqn is seperable and you get left with dy/(a*y^n + c) = dx , not an easy integral but if you are given specific values of your constants you will have a better chance.
 
  • #3
yes it is seperable. But this integral is tought too :)
 
  • #4
matlab can't solve it.

Should i trust MATLAB and not keep on trying to solve this ??
 
  • #5
As i said with arbitary n the integral is very difficult and you won't get very far with a pen and paper (if you want an exact solution).
I plugged this into the integrator and it gave me a solution, i haven't got access to MATLAB to try on that
 

1. What is a "Very Tough Nonlinear First Order Differential Equation"?

A "Very Tough Nonlinear First Order Differential Equation" is a type of mathematical equation that describes the relationship between a function and its derivatives. It is considered tough because it is nonlinear, meaning that the function and its derivatives are not proportional, and it is a first-order equation, meaning that it only involves the first derivative of the function.

2. What makes a "Very Tough Nonlinear First Order Differential Equation" difficult to solve?

The nonlinearity of the equation makes it difficult to solve because there is not a direct method for finding the solution. Additionally, the first-order nature of the equation means that it only involves the first derivative, making it harder to manipulate and solve compared to higher-order differential equations.

3. What are some real-world applications of "Very Tough Nonlinear First Order Differential Equations"?

These types of equations are commonly used in physics, engineering, and economics to model complex systems. They can be used to describe the behavior of physical systems like heat flow, electrical circuits, and chemical reactions. They are also useful in modeling economic systems like population growth and market dynamics.

4. What techniques are used to solve "Very Tough Nonlinear First Order Differential Equations"?

There are several techniques that can be used to solve these types of equations, such as the substitution method, the separation of variables method, and the integrating factor method. However, depending on the specific equation, some techniques may be more effective than others.

5. How important are "Very Tough Nonlinear First Order Differential Equations" in scientific research?

"Very Tough Nonlinear First Order Differential Equations" are essential in scientific research as they are used to model and understand complex phenomena in many different fields. They allow scientists to make predictions and analyze the behavior of systems that would be impossible to study otherwise. Additionally, the techniques used to solve these equations have applications in various areas of mathematics and engineering.

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