Solving Second Order nonlinear-ODE with mathematica

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SUMMARY

The discussion focuses on solving the second-order nonlinear ordinary differential equation (ODE) defined as y'' + 3y' = 1/(y^5) using Mathematica. The user initially attempts to use the DSolve function but encounters an error indicating that no symbolic solution exists. The recommended approach is to utilize the NDSolve function, which is suitable for obtaining numerical solutions, provided that all initial conditions, including y(0), are specified.

PREREQUISITES
  • Understanding of second-order nonlinear ordinary differential equations
  • Familiarity with Mathematica syntax and functions
  • Knowledge of initial conditions in differential equations
  • Basic concepts of numerical methods for solving ODEs
NEXT STEPS
  • Learn how to use Mathematica's NDSolve function for numerical solutions
  • Study the specification of initial conditions in differential equations
  • Explore graphical representation of solutions in Mathematica
  • Investigate methods for analyzing the behavior of nonlinear ODEs
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and engineers who are working with nonlinear differential equations and require practical solutions using Mathematica.

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Hi,
I am trying to solve a second order nonlinear eqn which is

y''+3y'=1/(y^5), y'(0)=0, using mathematica.
When I type
DSolve[y''[x]+3*y'[x]=(1/(y[x])^5) ,y'[0]==0,y[x],x]; I get "second-order nonlinear ordinary differential equation" as a result.
I don't understand what mistake I am making. I am not so much familiar to mathematica.

Could You help me to solve this eqn.
Thanks,
 
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Are you sure that this equation has an analytical solution? Try NDSolve instead.
 
The output you got from Mathematica means:
'Sorry, I did not find a symbolic solution for the problem'.
As the previous answer suggests, you should probably use
NDSove to find a numerical solution (for which graphical
representations can easily be created by Mathematica).
For this to work, you have to completely specify
initial conditions (i.e. you have not only to specify
an initial condition for y' but also one for y).
 
Last edited:

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