Very Tough Nonlinear First Order Differential Equation

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Homework Help Overview

The discussion revolves around a nonlinear first-order differential equation of the form y' = a*(y^n) + c, where a, n, and c are constants. Participants are exploring potential methods for solving this equation and discussing the challenges associated with it.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants mention the separability of the equation and suggest methods such as power series and integration techniques. There is also a discussion about the difficulty of the integral involved and the implications of using software like MATLAB for solving the equation.

Discussion Status

The conversation is ongoing, with participants expressing differing opinions on the feasibility of finding an analytic solution. Some suggest that specific values for the constants might simplify the problem, while others highlight the challenges of solving the integral by hand.

Contextual Notes

There is a mention of the limitations of MATLAB in solving the equation, and participants are questioning whether to rely on computational tools or continue attempting a manual solution.

sexycalibur
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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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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.
 
yes it is seperable. But this integral is tought too :)
 
matlab can't solve it.

Should i trust MATLAB and not keep on trying to solve this ??
 
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
 

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