Solving Second Order nonlinear-ODE with mathematica

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The user is attempting to solve a second-order nonlinear ordinary differential equation (ODE) using Mathematica but encounters an error indicating that no symbolic solution is available. The suggestion is to use NDSolve for a numerical solution instead, as it is more suitable for such equations. It is emphasized that complete initial conditions must be specified, including both y(0) and y'(0), for NDSolve to work effectively. The discussion highlights the limitations of DSolve in handling certain nonlinear equations. Overall, using NDSolve with proper initial conditions is recommended for finding a solution.
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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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