Solving Second Order nonlinear-ODE with mathematica

In summary, the conversation is about someone trying to solve a second order nonlinear equation using Mathematica. They are encountering difficulties and asking for help. The response suggests using NDSolve instead and explains the output received from Mathematica. The conversation ends with a suggestion to specify initial conditions for a numerical solution.
  • #1
minik
5
0
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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  • #2
Are you sure that this equation has an analytical solution? Try NDSolve instead.
 
  • #3
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:

1. How can I use Mathematica to solve a second order nonlinear ODE?

To solve a second order nonlinear ODE with Mathematica, you can use the NDSolve function. This function takes in the ODE, initial conditions, and any other necessary parameters, and returns a solution in the form of an InterpolatingFunction object.

2. What is the difference between a linear and a nonlinear ODE?

A linear ODE is one where the dependent variable and its derivatives are only raised to the first power. This allows for the use of superposition and other linear methods to solve the equation. Nonlinear ODEs, on the other hand, involve products and/or powers of the dependent variable and its derivatives, making them more difficult to solve analytically.

3. Can Mathematica handle boundary value problems for second order nonlinear ODEs?

Yes, Mathematica can handle boundary value problems for second order nonlinear ODEs using the ParametricNDSolve function. This function allows you to specify both initial and boundary conditions, giving a more complete solution to the ODE.

4. Are there any limitations to using Mathematica to solve second order nonlinear ODEs?

While Mathematica is a powerful tool for solving ODEs, there are some limitations. For example, it may not be able to find an analytical solution for every type of nonlinear ODE. Additionally, the solutions provided by Mathematica may not be in a form that is easily interpretable.

5. Can I plot the solution to a second order nonlinear ODE with Mathematica?

Yes, you can plot the solution to a second order nonlinear ODE using the Plot function. Simply input the InterpolatingFunction object returned by NDSolve as the function to plot, along with the desired range of values for the independent variable.

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