Find the general solution for x^2*y''-2y=0

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SUMMARY

The general solution for the differential equation x^2*y'' - 2y = 0 can be derived by rearranging it into the standard form y'' = (2y)/x^2. Users reported issues with the desolve function in their software, indicating that the correct input format is crucial for successful computation. Specifically, the desolve function requires a proper arrangement of the equation and sufficient arguments to process the solution. Consulting the manual for the specific software being used is essential for understanding the correct syntax and function usage.

PREREQUISITES
  • Understanding of second-order differential equations
  • Familiarity with the desolve function in mathematical software
  • Knowledge of manipulating differential equations into standard forms
  • Basic proficiency in using mathematical software manuals
NEXT STEPS
  • Research how to manipulate differential equations into standard forms
  • Learn the syntax and usage of the desolve function in your specific software
  • Explore examples of solving second-order differential equations
  • Consult the manual for your mathematical software for troubleshooting input errors
USEFUL FOR

Students, mathematicians, and anyone involved in solving differential equations, particularly those using mathematical software for computation.

Octavius1287
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I have searched for a long time and i can't find a clear answer

I want to find the general solution for x^2*y''-2y=0 using deslove and i typed it in as

desolve(x^2*y''-2y=0,y) and it says too few arguments
then i tried
desolve(x^2*y''-2y=0,y,x) same thing, then i switched the y ans the x didnt help

And i can't find any where the right format to use to solve this
 
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In cases like these, one must consult the manual.

Calculators and computers are notoriously balky about accepting any old input.
For your equation, you must manipulate it so that it becomes y'' = stuff.
 

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